-65 times the difference between a number and 79 is equal to the number plus 98 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. The first expression, [I]the difference between a number and 79[/I] means we subtract 79 from our arbitrary variable of x: x - 79 Next, -65 times the difference between a number and 79 means we multiply our result above by -65: -65(x - 79) The phrase [I]the number[/I] refers to the arbitrary variable x earlier. The number plus 98 means we add 98 to x: x + 98 Now, let's bring it all together. The phrase [I]is equal to[/I] means an equation. So we set -65(x - 79) equal to x + [B]98: -65(x - 79) = x + 98[/B] <-- This is our algebraic expression If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=-65%28x-79%29%3Dx%2B98&pl=Solve']type this equation into our search engine[/URL], and you get: x = [B]76.31818[/B]

1 - n = n - 1 Solve for [I]n[/I] in the equation 1 - n = n - 1 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables -n and n. To do that, we subtract n from both sides -n + 1 - n = n - 1 - n [SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE] -2n + 1 = -1 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 1 and -1. To do that, we subtract 1 from both sides -2n + 1 - 1 = -1 - 1 [SIZE=5][B]Step 4: Cancel 1 on the left side:[/B][/SIZE] -2n = -2 [SIZE=5][B]Step 5: Divide each side of the equation by -2[/B][/SIZE] -2n/-2 = -2/-2 n = [B]1 [URL='https://www.mathcelebrity.com/1unk.php?num=1-n%3Dn-1&pl=Solve']Source[/URL][/B]

1 hour and 54 minutes after 7:30 Let's take the easy and lazy way to solve this. 1 hour and 54 minutes is 6 minutes short of 2 hours So we add 2 hours to 7:30: 7:30 + 2 hours = 9:30 Then we subtract off the 6 minutes: 9:30 - 6 minutes = [B]9:24[/B]

1/2 of a number decreased by twice a number [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]1/2 of a number: x/2 [*]Twice a number means we multiply x by 2: 2x [*]The phrase [I]decreased by[/I] means we subtract [/LIST] [B]x/2 - 2x[/B]

1/4 of the difference of 6 and a number is 200 Take this [B]algebraic expression[/B] in 4 parts: [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]The difference of 6 and a number means we subtract x from 6: 6 - x [*]1/4 of the difference means we divide 6 - x by 4: (6 - x)/4 [*]Finally, the phrase [I]is[/I] means an equation, so we set (6 - x)/4 equal to 200 [/LIST] [B](6 - x)/4 = 200[/B]

1/6 of n subtracted from 3 1/6 of n: n/6 Subtracted from 3 means we subtract this expression from 3: [B]3 - n/6[/B]

1/a + 1/b = 1/2 for a Subtract 1/b from each side to solve this literal equation: 1/a + 1/b - 1/b = 1/2 - 1/b Cancel the 1/b on the left side, we get: 1/a = 1/2 - 1/b Rewrite the right side, using 2b as a common denominator: 1/a = (b - 2)/2b Cross multiply: a(b - 2) = 2b Divide each side by (b - 2) a = [B]2b/(b - 2)[/B]

1/n + 3/5 = 1 Subtract 3/5 from each side where 1 = 5/5 1/n + 3/5 - 3/5 = 5/5 - 3/5 1/n = 2/5 Cross multiply: 5 * 1 = 2 * n 2n = 5 Divide each side by 2: n = [B]5/2 or 2.5[/B]

104 subtracted from the quantity 6 times r is the same as r The quantity 6 times r means we multiply 6 by r: 6r 104 subtracted from 6r is written as: 6r - 104 [B]The phrase [I]is the same as[/I] means we have an equation. So we set 6r - 104 equal to r 6r - 104 = r[/B]

108 times a, reduced by 147 is k subtracted from 56 Take this algebraic expression in pieces: Step 1: 108 times a: 108a Step 2: Reduced by means subtract, so we subtract 47 from 108a: 108a - 47 Step 3: ksubtracted from 56: 56 - k Step 4: The phrase [I]is[/I] means equal to, so we set 108a - 47 equal to 56 - k [B]108a - 47 = 56 - k [MEDIA=youtube]KrY6uzKeeB0[/MEDIA][/B]

110 subtracted from the product of 244 and w is the product of r and 177 increased by 266 The product of 244 and w: 244w 110 subtracted from the product of 244 and w 244w - 110 the product of r and 177 177r the product of r and 177 increased by 266 177r + 266 The word [I]is[/I] means equal to, so we set 244w - 110 equal to 177r + 266 [B]244w - 110 = 177r + 266[/B]

12 is subtracted from d and the result is tripled 12 is subtracted from d: d - 12 the result is tripled means we multiply d - 12 by 3 [B]3(d - 12)[/B]

12 is subtracted from d and the result is tripled. 12 is subtracted from d: d - 12 The result is tripled means we multiply d - 12 by 3 [B]3(d - 12) [MEDIA=youtube]1xqWstiIDP0[/MEDIA][/B]

This is a symbol for a triple factorial. We have n!!! = n * (n - 3) * (n - 6) * ... * 1 Our subtraction of 3 never goes below one. 12!!! = [B]12 * 9 * 6 * 3 [MEDIA=youtube]xm2D7WxVjk8[/MEDIA] [/B]

Let G be green eyes and S be Stripes, and SG be Stripes and Green Eyes. [U]Set up an equation[/U] Total Cats = Green Eyes + Stripes - Green Eyes and Stripes 15 = G + 10 - 7 15 = G + 3 [U]Subtract 3 from each side:[/U] [B]G = 12[/B]

15 less than a number squared A number is denoted by an arbitrary variable, let's call it x. x Squared means we raise that number to a power of 2 x^2 15 less means we subtract [B]x^2 -15[/B]

15y + 13/c = m for y Subtract 13/c from each side to isolate the y term: 15y + 13/c - 13/c = m - 13/c Cancel the 13/c on the left side and we get 15y = m - 13/c Now, divide each side by 15 to isolate y: 15y/15 = (m - 13/c)/15 Cancel the 15 on the left side, and we get: y = [B](m - 13/c)/15[/B]

16 decreased by 3 times the sum of 3 and a number Take this algebraic expression in parts: [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. [*]The sum of 3 and a number: 3 + x [*]3 times the sum: 3(3 + x) [*]16 decreased by... means we subtract 3(3 + x) from 16 [/LIST] [B]3(3 + x) from 16[/B]

17 decreased by three times d equals c three times d means we multiply d by 3: 3d 17 decreased by three times d means we subtract 3d from 17 17 - 3d The word [I]equals[/I] means an equation, so we set 17 - 3d equal to c: [B]17 - 3d = c[/B]

18 - 6 & 1/9 = Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=18&frac2=6%261%2F9&pl=Subtract']fraction calculator[/URL], we get: [B]107/9 [URL='https://www.mathcelebrity.com/fraction.php?frac1=107%2F9&frac2=6%261%2F9&pl=Simplify']or[/URL] 11 & 8/9[/B]

19 decreased by the absolute value of c Take this algebraic expression in parts: [LIST] [*]Absolute value of c: |c| [*]19 decreased by the absolute value of c is found by subtracting |c| from 19 [/LIST] [B]19 - |c|[/B]

Let x be the first even integer. That means the next consecutive even integer must be x + 2. Set up our equation: x + (x + 2) = 118 Group x terms 2x + 2 = 118 Subtract 2 from each side 2x = 116 Divide each side by 2 x = 58 Which means the next consecutive even integer is 58 + 2 = 60 So our two consecutive even integers are [B]58, 60[/B] Check our work: 58 + 60 = 118

2 consecutive odd integers such that their product is 15 more than 3 times their sum. Let the first integer be n. The next odd, consecutive integer is n + 2. We are given the product is 15 more than 3 times their sum: n(n + 2) = 3(n + n + 2) + 15 Simplify each side: n^2 + 2n = 6n + 6 + 15 n^2 + 2n = 6n + 21 Subtract 6n from each side: n^2 - 4n - 21 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-4n-21%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get: n = (-3, 7) If we use -3, then the next consecutive odd integer is -3 + 2 = -1. So we have [B](-3, -1)[/B] If we use 7, then the next consecutive odd integer is 7 + 2 = 9. So we have [B](7, 9)[/B]

2 numbers that add up makes 5 but multiplied makes -36 Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*]x + y = 5 [*]xy = -36 [/LIST] Rearrange equation (1) by subtracting y from each side: [LIST=1] [*]x = 5 - y [*]xy = -36 [/LIST] Substitute equation (1) for x into equation (2): (5 - y)y = -36 5y - y^2 = -36 Add 36 to each side: -y^2 + 5y + 36 = 0 We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=-y%5E2%2B5y%2B36%3D0&pl=Solve+Quadratic+Equation&hintnum=0']type it in our search engine and solve[/URL] to get: y = ([B]-4, 9[/B]) We check our work for each equation: [LIST=1] [*]-4 + 9 = -5 [*]-4(9) = -36 [/LIST] They both check out

2 times a number subtracted by x The phrase [I]a number[/I] means an arbitrary variable, let's call it n. n 2 times a number means we multiply n by 2: 2n The phrase [I]subtracted by[/I] means we subtract 2n from x: [B]x - 2n[/B]

200 feet shorter than the height of a light house Let the height of a light house be h: h 200 fee shorter mean we subtract 200 from h: [B]h - 200[/B]

217 times u, reduced by 180 is the same as q. Take this algebraic expression pieces: Step 1: 217 times u We multiply the variable u by 217 217u Step 2: reduced by 180 Subtract 180 from 217u 217u - 180 The phrase [I]is the same as[/I] means an equation, so we set 217u - 180 equal to q [B]217u - 180 = q[/B]

223 subtracted from the quantity 350 times a is equal to b Take this algebraic expression in parts: [LIST] [*]the quantity 350 times a: 350a [*]223 subtracted from the quantity: 350a - 223 [*]The phrase [I]is equal to[/I] means an equation, so we set 350a - 223 equal to b [/LIST] [B]350a - 223 = b[/B]

Thrice of y means multiply y by 3 3y 23 decreased by 3y means we subtract 23 - 3y Is not equal to means we set up an equation with not equal sign 23 - 3y <> 15

231 is 248 subtracted from the quantity h times 128 Let's take this algebraic expression in parts: [LIST=1] [*]h times 128: 128h [*]24 subtracted from this: 128h - 248 [*]The word [I]is[/I] means an equation, so we set 128h - 248 equal to 231 [/LIST] [B]128h - 248 = 231[/B] <-- This is our algebraic expression If the problem asks you to solve for h, then you [URL='https://www.mathcelebrity.com/1unk.php?num=128h-248%3D231&pl=Solve']type in this equation into our search engine[/URL] and get: h = [B]3.742[/B]

249 equals 191 times c, decreased by 199 [U]Take this in pieces:[/U] 191 times c: 191c The phrase [I]decreased by[/I] means we subtract 199 from 191c: 191c - 199 We set this expression equal to 249: [B]191c - 199 = 249[/B] <-- This is our algebraic expression If you want to solve for c, type this equation into the search engine and we get: [B]c = 2.346[/B]

26 diminished by twice m Twice m means multiply m by 2 2m 26 diminished by twice m means subtract 2m from 26 [B]26 - 2m[/B]

26 students 15 like vanilla 16 like chocolate. 3 do not like either flavour. How many like both vanilla and chocolate Define our people: [LIST=1] [*]We have Vanilla Only [*]Chocolate Only [*]Both Vanilla and Chocolate [*]Neither Vanilla Nor Chocolate [*]Add up 1-4 to get our total [/LIST] Total = Vanilla Only + Chocolate Only - Vanilla and Chocolate + Neither 26 = 15 + 16 - V&C + 3 26 = 34 - V&C Subtract 34 from each side -V&C = -8 Multiply each side by -1 [B]V&C = 8[/B]

[U]A number means an arbitrary variable, let's call it x.[/U] [LIST] [*]x [/LIST] [U]Twice a number means multiply by 2[/U] [LIST] [*]2x [/LIST] [U]28 less than twice a number means we subtract 28[/U] [LIST] [*][B]2x - 28[/B] [/LIST]

2m - n/3 = 5m for n Subtract 2m from each side of the equation: 2m-n/3 - 2m = 5m - 2m -n/3 = 3m Multiply each side of the equation by -3 to isolate n: -3 * -n/3 = -3 * 3m n = [B]-9m[/B]

2n + 1 = n + 10 Solve for [I]n[/I] in the equation 2n + 1 = n + 10 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 2n and n. To do that, we subtract n from both sides 2n + 1 - n = n + 10 - n [SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE] n + 1 = 10 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 1 and 10. To do that, we subtract 1 from both sides n + 1 - 1 = 10 - 1 [SIZE=5][B]Step 4: Cancel 1 on the left side:[/B][/SIZE] n = [B]9[/B]

2n + 10 = 3n + 5 Solve for [I]n[/I] in the equation 2n + 10 = 3n + 5 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 2n and 3n. To do that, we subtract 3n from both sides 2n + 10 - 3n = 3n + 5 - 3n [SIZE=5][B]Step 2: Cancel 3n on the right side:[/B][/SIZE] -n + 10 = 5 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 10 and 5. To do that, we subtract 10 from both sides -n + 10 - 10 = 5 - 10 [SIZE=5][B]Step 4: Cancel 10 on the left side:[/B][/SIZE] -n = -5 [SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE] -1n/-1 = -5/-1 n = [B]5[/B]

2n + 8 - n = 20 Solve for [I]n[/I] in the equation 2n + 8 - n = 20 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 - 1)n = n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] n + 8 = + 20 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 8 and 20. To do that, we subtract 8 from both sides n + 8 - 8 = 20 - 8 [SIZE=5][B]Step 4: Cancel 8 on the left side:[/B][/SIZE] n = [B]12[/B]

2n + 8 = 24 Solve for [I]n[/I] in the equation 2n + 8 = 24 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 8 and 24. To do that, we subtract 8 from both sides 2n + 8 - 8 = 24 - 8 [SIZE=5][B]Step 2: Cancel 8 on the left side:[/B][/SIZE] 2n = 16 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2n/2 = 16/2 n = [B]8[/B]

2n = 4n Solve for [I]n[/I] in the equation 2n = 4n [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 2n and 4n. To do that, we subtract 4n from both sides 2n - 4n = 4n - 4n [SIZE=5][B]Step 2: Cancel 4n on the right side:[/B][/SIZE] -2n = 0 [SIZE=5][B]Step 3: Divide each side of the equation by -2[/B][/SIZE] -2n/-2 = 0/-2 n = [B]0[/B]

2x - b/y = 4c for y Subtract 2x from each side: 2x - 2x - b/y = 4c - 2x Cancel the 2x's on the left side and we get: -b/y = 4c - 2x Cross multiply: -b = y(4c - 2x) Divide each side by (4c - 2x): -b/(4c - 2x) = y(4c - 2x)/(4c - 2x) Cancel the (4c - 2x) on the right side and we get: [B]y = -b/(4c - 2x) [/B]

2x decreased by 15 is equal to -27 The phrase [I]decreased by[/I] 15 means we subtract 15 from 2x: 2x - 15 The phrase [I]is equal to[/I] means an equation, so we set 2x - 15 equal to -27 [B]2x - 15 = -27 [/B] <-- This is our algebraic expression To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D-27&pl=Solve']type 2x - 15 = -27 into the search engine[/URL].

2x^2+4x < 3x+6 Subtract 3x from both sides: 2x^2 + x < 6 Subtract 6 from both sides 2x^2 + x - 6 < 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=2x%5E2%2Bx-6&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: x < 1.5 and x < -2 When we take the intersection of these, it's [B]x < 1.5[/B]

2^n = 4^(n - 3) 2^n = (2^2)^(n - 3) (2^2)^(n - 3) = 2^2(n - 3) 2^n= 2^2(n - 3) Comparing exponents, we see that: n = 2(n - 3) n = 2n - 6 Subtract n from each side: n - n = 2n - n - 6 0 = n - 6 n = [B]6[/B]

3 decreased by 7 times a number A number signifies an arbitrary variable, let's call it x. 7 times a number: 7x 3 decreased by this means we subtract 7x [B]3 - 7x[/B]

3 is subtracted from 3/4 of g 3/4 of g means we multiply g by 3/4: 3g/4 Subtracted from means we subtract 3 from 3g/4 [B]3g/4 - 3[/B]

3 is subtracted from square of a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Square of a number means we raise x to the 2nd power: x^2 3 is subtracted from square of a number [B]x^2 - 3[/B]

3 is subtracted from the square of x Let's take this algebraic expression in two parts: Part 1: The square of x means we raise x to the power of 2: x^2 Part 2: 3 is subtracted means we subtract 3 from x^2 [B]x^2 - 3[/B]

3 less than a number times itself The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Itself means the same variable as above. So we have: x * x x^2 3 less than this means we subtract 3 from x^2: [B]x^2 - 3[/B]

3 subtracted from the cost of the book Let the cost of the book be b. We have: [B]b - 3[/B]

The difference of x and 5 means we subtract: x - 5 3 times the difference means we multiply (x - 5) by 3 3(x - 5) Is, means equal to, so we set our expression equal to 15 [B]3(x - 5) = 15 [/B] If you need to take it one step further to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3%28x-5%29%3D15&pl=Solve']equation calculator[/URL]

3 times the quantity 2 decreased by x is 9 The quantity 2 decreased by x. The phrase [I]decreased by[/I] means we subtract: 2 - x 3 times the quantity: 3(2 - x) The word [I]is[/I] means equal to, so we set 3(2 - x) equal to 9: [B]3(2 - x) = 9 [MEDIA=youtube]Hzyt_GajZA4[/MEDIA][/B]

3 times x minus y is 5 times the sum of y and 2 times x Take this algebraic expression in pieces: 3 times x: 3x Minus y means we subtract y from 3x 3x - y The sum of y and 2 times x mean we add y to 2 times x y + 2x 5 times the sum of y and 2 times x: 5(y + 2x) The word [I]is[/I] means an equation, so we set 3x - y equal to 5(y + 2x) [B]3x - y = 5(y + 2x)[/B]

30 is equal to thrice y decreased by z Thrice y means we multiply y by 3: 3y Decreased by z means we subtract z from 3y 3y - z The phrase [I]is[/I] means an equal to, so we set up an equation where 3y - z is equal to 30 [B]3y - z = 30[/B]

300 reduced by 5 times my age is 60 Let my age be a. We have: 5 times my age = 5a 300 reduced by 5 times my age means we subtract 5a from 300: 300 - 5a The word [I]is[/I] means an equation, so we set 300 - 5a equal to 60 to get our final algebraic expression: [B]300 - 5a = 60 [/B] If you have to solve for a, you [URL='https://www.mathcelebrity.com/1unk.php?num=300-5a%3D60&pl=Solve']type this equation into our search engine[/URL] and you get: a = [B]48[/B]

309 is the same as 93 subtracted from the quantity f times 123. The quantity f times 123: 123f Subtract 93: 123f - 93 The phrase [I]is the same as[/I] means an equation, so we set 123f - 93 equal to 309 [B]123f - 93 = 309[/B] <-- This is our algebraic expression If you wish to solve for f, [URL='https://www.mathcelebrity.com/1unk.php?num=123f-93%3D309&pl=Solve']type this equation into the search engine[/URL], and we get f = 3.2683.

31,29,24,22,17 what comes next We see that each sequence term alternates between subtracting 2 and subtracting 5. Since the last term, 17, was found by subtracting 5, our next term is found by subtracting 2 from 17: 17 - 2 = [B]15[/B]

324 times z, reduced by 12 is z. Take this algebraic expression in pieces: 324 [I]times[/I] z means we multiply 324 by the variable z. 324z [I]Reduced by[/I] 12 means we subtract 12 from 324z 324z - 12 The word [I]is[/I] means we have an equation, so we set 324z - 12 equal to z [B]324z - 12 = z [/B] <-- This is our algebraic expression

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were In bus? Subtract the 7 students in cars, and we're left with: 331 - 7 = 324 students in buses. 324 students / 6 buses = [B]54 students in each bus[/B].

36, 34, 30, 28, 24 … It alternates like this: -2 -4 -2 -4 Next numbers should subtract 2 24 - 2 = [B]22 [MEDIA=youtube]nfkxUcJZLU0[/MEDIA][/B]

[U]q times 146:[/U] 146q [U]365 subtracted from that:[/U] 146q - 365 [U]Is the same as means equal to, so we have:[/U] [B]146q - 365 = w[/B]

3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b Expand term 1: 3abc^4/12a^3(b^3c^2)^2 3abc^4/12a^3b^6c^4 Now simplify term 1: 3/12 = 1/4 c^4 terms cancel Subtract powers from variables since the denominator powers are higher: b^(6 - 1) = b^5 a^(3 - 1) = a^2 1/4a^2b^5 Now simplify term 2: 8ab^-4c/4a^2b 8/4 = 2 2c/a^(2 - 1)b^(1 - -4) 2c/ab^5 Now multiply simplified term 1 times simplified term 2: 1/4a^2b^5 * 2c/ab^5 (1 * 2c)/(4a^2b^5 * ab^5) 2c/4a^(2 + 1)b^(5 + 5) 2c/4a^3b^10 2/4 = 1/2, so we have: [B]c/2a^3b^10[/B]

3f,subtract g from the result, then divide what you have by h Take this algebraic expression in pieces: 3f subtract g means we subtract the variable g from the expression 3f: 3f - g Divide what we have by h, means we take the result above, 3f - g, and divide it by h: [B](3f - g)/h[/B]

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5 This is an algebraic expression. Let's take this algebraic expression in 5 parts: [LIST=1] [*]The sum of 2x and 1 means we add 1 to 2x: 2x + 1 [*]2 times the sum of 2x and 1: 2(2x + 1) [*]3x less than the sum of 2x and 1 means we subtract 3x from 2(2x + 1): 2(2x + 1) - 3x [*]The sum of 2 and 5 means we add 5 to 2: 2 + 5 [*]Finally, the phrase [I]equal[/I] means an equation, so we set #3 equal to #4 [/LIST] Our algebraic expression is: [B]2(2x + 1) - 3x = 2 + 5[/B] Now, some problems may ask you to simplify. In this case, we multiply through and group like terms: 4x + 2 - 3x = 7 [B]x + 2 = 7 <-- This is our simplified algebraic expression [/B] Now, what if the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B2%3D7&pl=Solve']you type this into our search engine[/URL] and get: x =[B] 5 [MEDIA=youtube]3hzyc2NPCGI[/MEDIA][/B]

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section of a picture frame. Determine the area inside the wooden frame. Area inside forms a square, with a length of 30 - 3 - 3 = 24. We subtract 3 twice, because we account for 2 rectangular strips with a width of 3. Area of a square is side * side. So we have 24 * 24 = [B]576cm^2[/B]

4 times a number cubed decreased by 7 A number is denoted as an arbitrary variable, let's call it x x Cubed means raise x to the third power x^3 Decreased by 7 means subtract 7 x^3 - 7

4 times b increased by 9 minus twice y Take this algebraic expression in parts: Step 1: 4 times b means we multiply the variable b by 4: 4b Step 2: Increased by 9 means we add 9 to 4b: 4b + 9 Step 3: Twice y means we multiply the variable y by 2: 2y Step 4: The phrase [I]minus[/I] means we subtract 2y from 4b + 9 [B]4b + 9 - 2y[/B]

4 times the difference of 6 times a number and 7 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 6 times a number 6x The difference of 6x and 7 means we subtract 7 from 6x: 6x - 7 Now we multiply this difference by 4: [B]4(6x - 7)[/B]

4n - 8 = n + 1 Solve for [I]n[/I] in the equation 4n - 8 = n + 1 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4n and n. To do that, we subtract n from both sides 4n - 8 - n = n + 1 - n [SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE] 3n - 8 = 1 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -8 and 1. To do that, we add 8 to both sides 3n - 8 + 8 = 1 + 8 [SIZE=5][B]Step 4: Cancel 8 on the left side:[/B][/SIZE] 3n = 9 [SIZE=5][B]Step 5: Divide each side of the equation by 3[/B][/SIZE] 3n/3 = 9/3 n = [B]3[/B]

4 subtracted from 6 times a number is 32. Take this algebraic expression in pieces. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 6 times this number means we multiply by x by 6 6x 4 subtracted from this expression means we subtract 4 6x - 4 The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32 [B]6x - 4 = 32 [/B] If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].

Subtract 5 from each side: -8|-2n| = -80 Divide each side by -8 |-2n| = 10 Since this is an absolute value equation, we need to setup two equations: -2n = 10 -2n = -10 Solving for the first one by dividing each side by -2, we get: n = -5 Solving for the second one by dividing each side by -2, we get: n = 5

5 diminished by twice the sum of a and b Take this algebraic expression in parts: [LIST] [*]The sum of a and b: a + b [*]Twice the sum means we multiply a + b by 2: 2(a + b) [*]5 diminished by twice the sum means we subtract 2(a + b) from 5 [/LIST] [B]5 - 2(a + b)[/B]

5 less than x means we subtract 5 from x. x - 5 Is, means equal to, so we set x - 5 equal to y x - 5 = y

5 squared minus a number x 5 squared is written as 5^2 Minus a number x means we subtract the variable x [B]5^2 - x[/B]

5 subtracted from 3 times a number is 44. The problem asks for an algebraic expression. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 3 times this number is 3x. 5 subtracted from this is written as 3x - 5. The phrase [I]is[/I] means an equation, so we set 3x - 5 equal to 44 [B]3x - 5 = 44[/B]

5 times g reduced by the square of h Take this algebraic expression in pieces: [LIST=1] [*]5 times g means we multiply g by 5: 5g [*]The square of h means we raise h to the 2nd power: h^2 [*]5 times g reduced by the square of h means we subtract h^2 from 5g: [/LIST] [B]5g - h^2[/B]

5/8 Of a class are boys. what fraction of the class are girls? The total class equals 1. Since 5/8 are boys, we subtract 5/8 from 1: 1 - 5/8 But we can write 1 as 8/8. So we have 8/8 - 5/8 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F8&frac2=5%2F8&pl=Subtract']Type this fraction operation into our search engine[/URL] and we get: [B]3/8[/B] are girls

5/9v+w=z,for v Subtract w from each side: 5/9v = z - w Multiply each side by 9/5 [B]v = 9(z - w)/5 [MEDIA=youtube]zZo_HveA3AY[/MEDIA][/B]

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there? Assumptions: [LIST] [*]Let the number of adults be a [*]Let the number of kids be k [/LIST] Given with assumptions: [LIST=1] [*]a + k = 508 [*]2a + 1.25k = 885.50 (since cost = price * quantity) [/LIST] Rearrange equation (1) by subtracting c from each side to isolate a: [LIST=1] [*]a = 508 - k [*]2a + 1.25k = 885.50 [/LIST] Substitute equation (1) into equation (2): 2(508 - k) + 1.25k = 885.50 Multiply through: 1016 - 2k + 1.25k = 885.50 1016 - 0.75k = 885.50 To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get: k = [B]174[/B] Now, to solve for a, we substitute k = 174 into equation 1 above: a = 508 - 174 a = [B]334[/B]

A number is denoted as an arbitrary variable, let's call it x. Twice a number means we multiply by 2, so 2x. 51 decreased by twice a number means we subtract 2x from 51 [B]51 - 2x [MEDIA=youtube]xqZzYvxmj5w[/MEDIA][/B]

6 diminished by twice x is at most 8 Twice x means we multiply x by 2: 2x 6 diminished by twice x means we subtract 2x from 6: 6 - 2x The phrase [I]is at most[/I] is an inequality using the sign <=, so we have: [B]6 - 2x <= 8[/B]

6 is subtracted from 3/5 of g 3/5 of g: 3g/5 6 is subtracted from 3/5 of g: [B]3g/5 - 6[/B]

6 subtracted from the product of 5 and a number is 68 Take this algebraic expression in parts. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The product of 5 and this number is: 5x We subtract 6 from 5x: 5x - 6 The phrase [I]is[/I] means an equation, so we set 5x - 6 equal to 68 [B]5x - 6 = 68[/B]

6 times j squared minus twice j squared j squared means we raise the variable j to the power of 2: j^2 6 times j squared means we multiply j^2 by 6: 6j^2 Twice j squared means we multiply j^2 by 2: 2j^2 The word [I]minus[/I] means we subtract 2j^2 from 6j^2 6j^2 - 2j^2 So if you must simplify, we group like terms and get: (6 - 2)j^2 [B]4j^2[/B]

6 times the sum of a number and 5 is 16 A number represents an arbitrary variable, let's call it x x The sum of x and 5 x + 5 6 times the sum of x and 5 6(x + 5) Is means equal to, so set 6(x + 5) equal to 16 [B]6(x + 5) = 16 <-- This is our algebraic expression Solve for x[/B] Multiply through: 6x + 30 = 16 Subtract 30 from each side: 6x - 30 + 30 = 16 - 30 6x = -14 Divide each side by 6 6x/6 = -14/6 Simplify this fraction by dividing top and bottom by 2: x = [B]-7/3 [MEDIA=youtube]oEx5dsYK7DY[/MEDIA][/B]

Set up an equation where h is Helena's age. h + 24 = 63 [URL='http://www.mathcelebrity.com/1unk.php?num=h%2B24%3D63&pl=Solve']Subtract 24 from each side[/URL] h = 39

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44. The phrase [I]difference between[/I] means we subtract 44 from a: a - 44 The phrase [I]64 is[/I] means an equation, so we set a - 44 equal to 64 [B]a - 44 = 64 <-- This is our algebraic expression [/B] If you want to solve for a, then we [URL='https://www.mathcelebrity.com/1unk.php?num=a-44%3D64&pl=Solve']type this expression into our search engine[/URL] and get: [B]a = 108[/B]

Let Tim's age be a. Twice that is 2a. 67 less than that means we subtract: 2a - 67

-2 times a number x is written as -2x. Less means subtract, so we have 7 less than this is -2x - 7. Finally, greater than or equal to is >=, so our expression becomes: -2x - 7 >= 41

-2 times a number x is denoted as -2x. 7 less than that means we subtract 7: -2x - 7 Finally, that entire expression is greater than or equal to 41 -2x - 7 >= 41

-2 times a number x is denoted as -2x. 7 less means we subtract, so 7 less than that is -2x - 7. Finally, that entire expression is greater than or equal to 41 -2x - 7 >= 41

7 subtracted from x cubed x cubed means x raised to the 3rd power x^3 7 subtracted from this [B]x^3 - 7[/B]

7 times a number and 2 is equal to 4 times a number decreased by 8 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 7 times a number: 7x and 2 means we add 2: 7x + 2 4 times a number 4x decreased by 8 means we subtract 8: 4x - 8 The phrase [I]is equal to[/I] means an equation, so we set 7x + 2 equal to 4x - 8: [B]7x + 2 = 4x - 8[/B]

7 times the quantity of 3 times a number reduced by 10 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. x 3 times a number: 3x Reduced by 10 means we subtract 10: 3x - 10 7 times this quantity: [B]7(3x - 10)[/B]

Let Carlos's age be a. Twice a means we multiply by 2 2a 70 decreased by that amount means we subtract: [B]70 - 2a[/B]

76 decreased by twice a number. Use the variable n to represent the unknown number. Twice a number (n) means we multiply the unknown number n by 2: 2n 76 decreased by twice a number means we subtract 2n from 76 using the (-) operator [B]76 - 2n[/B]

76 subtracted from p is equal to the total of g and 227 We've got two algebraic expressions. Take them in pieces: Part 1: 76 subtracted from p We subtract 76 from the variable p p - 76 Part 2: The total of g and 227 The total means a sum, so we add 227 to g g + 227 Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other: [B]p - 76 = g + 227[/B]

8 is subtracted from 3/5 of f 3/5 of f: 3f/5 8 subtracted from this: [B]3f/5 - 8[/B]

8 is subtracted from the square of x Take this algebraic expression in parts: [LIST] [*]The square of x means we raise x to the power of 2: x^2 [*]8 subtracted from the square of x is found by subtracting 8 from x^2 [/LIST] [B]x^2 - 8[/B]

Thrice a number means we multiply by 3. A number means an arbitrary variable, let's call it x 3x 8 is subtracted from 3x [B]3x - 8[/B]

Twice a number: [LIST] [*]Choose an arbitrary variable, let's call it x [*]Twice x means multiply by 2 [*]2x [/LIST] 8 subtracted from 2x: [B]2x - 8[/B]

8 less than triple the difference of 2x and 6 The [I]difference[/I] of 2x and 6 means we [B]subtract[/B] 6 from 2x 2x - 6 [I]Triple[/I] this difference means we [B]multiply by 3[/B] 3(2x - 6) 8 [I]less[/I] means we [B]subtract 8 from this expression 3(2x - 6) - 8[/B]

8 taken away from y This is an algebraic expression. The phrase [I]taken away[/I] means we subtract 8 from y: [B]y - 8[/B]

8 times the difference of 5y and 3 The difference of 5y and 3 means we subtract 3 from 5y: 5y - 3 8 times the difference means we multiply (5y - 3) by 8: [B]8(5y - 3)[/B]

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is the number? Let the number be n. We're given two expressions: [LIST=1] [*]8(n - 2) [I]difference means we subtract[/I] [*]3(n + 3) [I]sum means we add[/I] [/LIST] The phrase [I]is the same as[/I] mean an equation. So we set the first expression equal to the second expression: 8(n - 2) = 3(n + 3) To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=8%28n-2%29%3D3%28n%2B3%29&pl=Solve']type it in our search engine[/URL] and we see that: n =[B] 5[/B]

9 is subtracted from four fifths of y Four fifths of y: 4/5y Subtract 9 [B]4/5y - 9[/B]

9 less than 5 times a number is 3 more than 2x The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x 5 times a number means we multiply x by 5: 5x 9 less than 5x means we subtract 9 from 5x: 5x - 9 3 more than 2x means we add 3 to 2x: 2x + 3 The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3: [B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B] [B][/B] If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get: x = [B]4[/B]

9 less than thrice x Thrice x means multiply x by 3 3x 9 less than that means subtract 9 [B]3x - 9[/B]

9 less than twice x is twice y Twice x means we multiply x by 2: 2x 9 less than Twice x means we subtract 9 from 2x 2x - 9 Twice y means we multiply y by 2: 2y The word [I]is[/I] means equal to, so we set 2x - 9 equal to 2y: [B]2x - 9 = 2y[/B]

9 subtracted from the product of 3 and a number is greater than or equal to 16 [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]The product of 3 and a number means we multiply 3 times x: 3x [*]9 subtracted from the product: 3x - 9 [*]The phrase is greater than or equal to means an inequality. So we set up an inequality with >= for the greater than or equal to sign in relation to 3x - 9 and 16 [/LIST] Our algebraic expression (inequality) becomes: [B]3x - 19 >= 16[/B]

9 times a number is that number minus 10 The phrase [I]a number[/I] means we define a random/arbitrary variable, let's call it x: x 9 times a number means we multiply x by 9: 9x The phrase [I]that number[/I] refers back to the original arbitrary variable we defined above, which is x: x That number minus 10 means we subtract 10 from x: x - 10 The word [I]is[/I] means equal to, so we set 9x equal to x - 10 [B]9x = x - 10[/B]

963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs? Set up equation to represent the total animals on the farm Total Animals = Cows + Pigs + Sheep Now plug in what is given 963 = 406 + Pigs + 159 Simplify: Pigs + 565 = 963 Subtract 565 from each side [B]Pigs = 398[/B]

9x is subtracted from the sum of 3y and 4 The sum of 3y and 4 3y + 4 9x is subtracted from the sum of 3y and 4 [B]3y + 4 - 9x[/B]

a + b + c = 180 for b We have a literal equation. Subtract (a + c) from each side of the equation to isolate b: a + b + c - (a + c) = 180 - (a + c) The (a + c) cancels on the left side, so we have: [B]b = 180 - (a + c)[/B] or, distributing the negative sign: [B]b = 180 - a - c[/B]

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey? [U]Set up the relationship of still water speed and downstream speed[/U] Speed down stream = Speed in still water + speed of the current Speed down stream = x+2 Therefore: Speed upstream =x - 2 Since distance = rate * time, we rearrange to get time = Distance/rate: 15/(x+ 2) + 15 /(x- 2) = 3 Multiply each side by 1/3 and we get: 5/(x + 2) + 5/(x - 2) = 1 Using a common denominator of (x + 2)(x - 2), we get: 5(x - 2)/(x + 2)(x - 2) + 5(x + 2)/(x + 2)(x - 2) (5x - 10 + 5x + 10)/5(x - 2)/(x + 2)(x - 2) 10x = (x+2)(x-2) We multiply through on the right side to get: 10x = x^2 - 4 Subtract 10x from each side: x^2 - 10x - 4 = 0 This is a quadratic equation. To solve it, [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-10x-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine[/URL] and we get: Speed of the boat in still water =X=5 +- sq. Root of 29 kmph We only want the positive solution: x = 5 + sqrt(29) x = 10.38 [U]Calculate time for upstream journey:[/U] Time for upstream journey = 15/(10.38 - 2) Time for upstream journey = 15/(8.38) Time for upstream journey = [B]1.79[/B] [U]Calculate time for downstream journey:[/U] Time for downstream journey = 15/(10.38 + 2) Time for downstream journey = 15/(12.38) Time for downstream journey = [B]1.21[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800? Let x be the number of $24 tickets, and y be the number of $40 tickets. We have: [LIST=1] [*]24x + 40y = 188,800 [*]x + y = 6,000 [*]Rearrange (2) to solve for x: x = 6000 - y [*]Plug in (3) to (1): [/LIST] 24(6000 - y) + 40y = 188800 144,000 - 24y + 40y = 188,800 16y + 144,000 = 188,800 Subtract 144,000 from each side: 16y = 44,800 Divide each side by 16 y = 2,800 ($40 tickets) Plug this into (2) x + 2,800 = 6000 Subtract 2,800 from each side: x = 3,200 ($24 tickets)

a 9-foot rope is cut into two pieces one piece is x feet express the length of the other piece in terms of x Piece 1 + Piece 2 = 9 Piece 1 = x x + Piece 2 = 9 Subtracting x from each side, we get: x - x + Piece 2 = 9 - x Cancel the x's on the left side, we get: Piece 2 = [B]9 - x [/B] Check our work: x + 9 - x ? 9 9 = 9

A bag contains 10 red balls, 10 green balls and 6 white balls. Two balls are drawn at random from the bag without replacement. What is the probability that they are of different colours? [LIST] [*]The key phrase here is [I]without replacement[/I]. [*]First, it's easier to find the probability of both colors matching, and then subtracting that from 1. [/LIST] We want 1 - (P(Red-Red) + P(Green-Green) + P(White-White)). So we have the following: [U]Find the probability of both colors matching[/U] P(Red-Red) = 10/26 * 9/25 = 0.138462 P(Green-Green) = 10/26 * 9/25 = 0.138462 P(White-White) = 6/26 * 5/25 = 0.046154 P(Red-Red) + P(Green-Green) + P(White-White) = 0.13846 + 0.13846 + 0.046154 = 0.3231 Now, we want to take the complement of this probability which is no colors matching, so we have: P(Both Different Colors) = 1 - P(Same Colors) P(Both Different Colors) = 1 - 0.3231 P(Both Different Colors) = [B]0.6769[/B]

A barn contains cows, ducks, and a 3-legged dog named Tripod. There are twice as many cows as ducks in the barn and a total of 313 legs. How many ducks are there in the barn? [LIST] [*]Let the number of ducks be d. Duck legs = 2 * d = 2d [*]Number of cows = 2d. Cow legs = 4 * 2d = 8d [*]1 dog Tripod has 3 legs [/LIST] Total legs: 2d + 8d + 3 = 313 Solve for [I]d[/I] in the equation 2d + 8d + 3 = 313 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (2 + 8)d = 10d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 10d + 3 = + 313 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 313. To do that, we subtract 3 from both sides 10d + 3 - 3 = 313 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 10d = 310 [SIZE=5][B]Step 5: Divide each side of the equation by 10[/B][/SIZE] 10d/10 = 310/10 d = [B]31[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=2d%2B8d%2B3%3D313&pl=Solve']Source[/URL]

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441? Let the number of tickets above 42 be t. A few things to note on this question: [LIST] [*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality. [*]Earnings = Price * Quantity [/LIST] We're given: Earnings = 4.50 * 42 + 4.5t >= 441 Earnings = 189 + 4.5t >= 441 We want to solve this inequality for t: Solve for [I]t[/I] in the inequality 189 + 4.5t ≥ 441 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 189 and 441. To do that, we subtract 189 from both sides 4.5t + 189 - 189 ≥ 441 - 189 [SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE] 4.5t ≥ 252 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE] 4.5t/4.5 ≥ 252.4.5 [B]t ≥ 56[/B]

A baseball player gets 12 hits in 40 at bats. What percent are hits, and what percent are not hits? Percent Hits = 12/40 Using our [URL='http://www.mathcelebrity.com/perc.php?num=12&den=40&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']percent calculator[/URL], we get [B]30%[/B] Since you either get a hit or you don't, we subtract 30% from 100% to find the percent of not hits: Percent Not Hits = 100 - 30% = [B]70%[/B]

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each. [B][U]Set up Cost Function C(b) where b is the number of books:[/U][/B] C(b) = Fixed Cost + Variable Cost x Number of Units C(b) = 180,000 + 25(b) [B]Set up Revenue Function R(b):[/B] R(b) = 40b Set them equal to each other 180,000 + 25b = 40b Subtract 25b from each side: 15b = 180,000 Divide each side by 15 [B]b = 12,000 for break even[/B]

A bowl contains 45 oranges. If ⅔ of the oranges are bad; how many are good? Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=2%2F3&pl=Subtract']fraction operator calculator[/URL], we see that: 1 - 2/3 = 1/3 of the oranges are good. We want 1/3 of 45. [URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/3&pl=Multiply']Typing this expression into our search engine[/URL], we get: [B]15 good oranges[/B]

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils. Removed means we subtract from the total. So Our equation is: x - 6 = 54 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-6%3D54&pl=Solve']type it in our search engine [/URL]and we get: x = [B]60[/B]

A box has y oranges. 5 oranges are rotten and removed. The remaining oranges are placed equally into 2 containers . Each container has ______oranges Remove 5 rotten oranges means we subtract 5 from y: y - 5 If each of the two remaining boxes contains an equal amount of the remaining oranges, we have: [B](y - 5)/2[/B] oranges in each box

A boy has 6 toys he loses 3. How many does the boy have? We subtract 3 from 6 since losing means less, and we have: 6 - 3 = [B]3[/B]

A boy has m mangoes. He sells three of them write down an expression to represent how much he now has. When the boy sells the mangos, he has less. So we subtract 3 from m to get: [B]m - 3[/B]

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years? Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t: B(t) = 19,000(1-0.3)^t Simplifying this, we get: B(t) = 19,000(0.7)^t <-- I[I]f an asset decreases by 30%, it keeps 70% of it's value from the prior period[/I] The problem asks for B(4): B(4) = 19,000(0.7)^4 B(4) = 19,000(0.2401) B(4) = [B]4,561.90[/B]

A car repair bill was $441. This included $153 for parts and four hours of labor . Find the hourly rate I was charge for labor Subtract the cost of parts from the total repair bill to get the labor cost: Labor Cost = Total Bill - Parts Cost Labor Cost = 441 - 153 Labor Cost = 288 Labor Cost can be broken down into Labor divided by hours Hourly Labor Rate = Labor Cost / Labor Hours Hourly Labor Rate = = 288 / 4 Hourly Labor Rate = [B]72[/B]

A carpenter bought a piece of wood that was 43.32 centimeters long. Then she sawed 5.26 centimeters off the end. How long is the piece of wood now? When you saw off the end, the length decrease. So we subtract: New length = Original length - Sawed piec New length = 43.32 - 5.26 New length = [B]38.06[/B]

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25¢ per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned? Calculate the cost of the staircase cleaning. Staircase cost = $1.30 * steps Staircase cost = $1.30 * 14 Staircase cost = $18.20 Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet. Carpet cost = $253.95 - $18.20 Carpet cost = $235.75 Now, the remaining carpet cost can be written as: 75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned Multiply through and simplify: 75 + 0.25s - 45 = $235.75 Combine like terms: 0.25s + 30 = 235.75 [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B30%3D235.75&pl=Solve']Type this equation into our search engine[/URL] to solve for s, and we get: s = [B]823[/B]

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have? Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations: [LIST=1] [*]a + b = 44 [*]10a + 20b = 730 [/LIST] We rearrange equation 1 in terms of a. We subtract b from each side and we get: [LIST=1] [*]a = 44 - b [*]10a + 20b = 730 [/LIST] Now we substitute equation (1) for a into equation (2): 10(44 - b) + 20b = 730 Multiply through to remove the parentheses: 440 - 10b + 20b = 730 Group like terms: 440 + 10b = 730 Now, to solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=440%2B10b%3D730&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]29 [/B] To get a, we take b = 29 and substitute it into equation (1) above: a = 44 - 29 a = [B]15 [/B] So we have [B]15 ten-dollar bills[/B] and [B]29 twenty-dollar bills[/B]

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 per month. However, if you go over your 5 GB of data in a month, you have to pay an extra $10 for each GB. How many GB would be used to make both plans cost the same? Let g be the number of GB. The limited plan has a cost as follows: C = 10(g - 5) + 55 C = 10g - 50 + 55 C = 10g + 5 We want to set the limited plan equal to the unlimited plan and solve for g: 10g + 5 = 70 Solve for [I]g[/I] in the equation 10g + 5 = 70 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 5 and 70. To do that, we subtract 5 from both sides 10g + 5 - 5 = 70 - 5 [SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE] 10g = 65 [SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE] 10g/10 = 65/10 g = [B]6.5[/B] Check our work for g = 6.5: 10(6.5) + 5 65 + 5 70

A certain group of woman has a 0.69% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness? 0.69% = 0.0069. There exists a statistics theorem for an event A that states: P(A) + P(A') = 1 where A' is the event not happening In this case, A is the woman having red/green color blindness. So A' is the woman [U][B][I]not[/I][/B][/U][I] having red/green color blindness[/I] So we have: 0.0069 + P(A') = 1 Subtract 0.0069 from each side, we get: P(A') = 1 - 0.0069 P(A') = [B]0.9931[/B]

Let x be the number. We have: x^2 + x = 30 Subtract 30 from each side: x^2 + x - 30 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-30%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get potential solutions of: [B]x = 5 or x = -6[/B] Check 5: 5 + 5^2 = 5 + 25 = [B]30[/B] Check -6 -6 + -6^2 = -6 + 36 = [B]30[/B]

A checking account is set up with an initial balance of $2400 and $200 are removed from the account each month for rent right and equation who solution is the number of months and it takes for the account balance to reach 1000 200 is removed, so we subtract. Let m be the number of months. We want the following equation: [B]2400 - 200m = 1000 [/B] Now, we want to solve this equation for m. So [URL='https://www.mathcelebrity.com/1unk.php?num=2400-200m%3D1000&pl=Solve']we type it in our search engine[/URL] and we get: m = [B]7[/B]

A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom. Take this one piece at a time: [LIST] [*]We start with x students [*]9 of them went home. This means we have 9 less students. So we subtract 9 from x: x - 9 [*]The phrase [I]there are now[/I] means an equation, so we set x - 9 equal to 27 [/LIST] x - 9 = 27 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our search engine[/URL] and we get: x = [B]36[/B]

A company has 12,600 employees. Of these, 1/4 drive alone to work, 1/6 car pool, 1/8 use public transportation, 1/9 cycle, and the remainder use other methods of transportation. How many employees use each method of transportation? Find the remainder fraction: Remainder = 1 - (1/4 + 1/6 + 1/8 + 1/9) The least common multiple of 4, 6, 8, 9 is 72. So we divide 72 by each fraction denominator to get our multiplier: 1/4 = 18/72 1/6 = 12/72 1/8 = 9/72 1/9 = 8/72 Add those all up: (18 + 12 + 9 + 8)/72 47/72 Now subtract the other methods out from 1 to get the remainder of who use other methods: Remainder = 1 - 47/72 Since 1 = 72/72, we have: (72 - 47)/72 [B]25/72[/B]

A company has 95 employees. 4 get sacked. 57 quit. 52 are hired. How many employees are there now? Take this in pieces [LIST=1] [*]We start with 95 employees [*]4 get sacked (fired). So we subtract: 95 - 4 = 91 [*]57 quit. We subtract: 91 - 57 = 34 [*]52 are hired. We add: 34 + 52 = [B]86 employees[/B] [/LIST]

A dad gave his 3 sons each the same amount of money in an envelope. He took $20 from one son for getting a D on a math test and he gave another son an extra $35 for doing extra chores. Combined, the sons had $81. Figure out how much each son had. Let x, y, and z be the money each son received. To begin, x = y = z. But then, Dad took 20 from son X and gave it to son Y. So now, x = y - 20 Next, he gave Son Z an extra $35 for chores So z is now y + 35 since y and z used to be equal Combined, they all have 81. x + y + z = 181 But with the changes, it is: (y - 20) + y + (y + 35) Combine like terms: 3y - 20 + 35 = 81 3y + 15 = 81 Subtract 15 from each side: 3y = 66 Divide each side by 3 to isolate y y = 22 Since x = y - 20, x = 2 Since z = y + 35, we have z = 57 Checking our work, 2 + 22 + 57 = 81.

A family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three hours and then 20$ for each additional hour. Suppose the family can spend $110 for the canoe rental. What is the maximum number of hours the family can rent the canoe? IF we subtract the $50 for the first 3 hours, we get: 110 - 50 = 60 remaining Each additional hour is 20, so the max number of hours we can rent the canoe is $60/20 = 3 hours additional plus the original 3 hours is [B]6 hours[/B]

A family of 4 spent $78 at the exhibition. They spent $22 on rides and the rest on entrance fees. How much was the entrance fee per person We need to find the entrance fee per person. So subtract the cost of rides from the total spend: Entrance Fees = Total Spend - Cost of Rides Entrance Fees = 78 - 22 Entrance Fees = 56 [U]Now find the entrance fee per person:[/U] Entrance Fee Per Person = Entrance Fees / Total People in the Family Entrance Fee Per Person =56/4 Entrance Fee Per Person = [B]14[/B]

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers Let the first number be a and the second number be b. We have: [LIST=1] [*]a + 2b = 7 [*]2a + b = 23 [/LIST] Rearrange (1) into (3) (3) a = 7 - 2b Substitute (3) into (2): 2(7 - 2b) + b = 23 Multiply through: 14 - 4b + b = 23 Combine like terms: 14 - 3b = 23 Subtract 14 from each side: -3b = 9 Divide each side by -3 [B]b = -3[/B] Substitute this into (3) a = 7 - 2b a = 7 - 2(-3) a = 7 + 6 [B]a = 13[/B] [B](a, b) = (13, -3)[/B]

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will its dimensions be? A flower bed has a rectangle shape, so the area is: A = lw We are given l = w + 3 Plugging in our numbers given to us, we have: 108 = w(w + 3) w^2 + 3w = 108 Subtract 108 from each side: w^2 + 3w - 108 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B3w-108%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get: w = (9, -12) Since length cannot be negative, w = 9. And l = 9 + 3 --> l = 12 So we have [B](l, w) = (12, 9)[/B] Checking our work, we have: A = (12)9 A = 108 <-- Match!

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? Let the number of drinks be d. Let the number of salads be s. We're given two equations: [LIST=1] [*]2d + 6.50s = 836.50 [*]d + s = 209 [/LIST] We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides: d + s - s = 209 - s Cancel the s's, we get: d = 209 - s So we have the following system of equations: [LIST=1] [*]2d + 6.50s = 836.50 [*]d = 209 - s [/LIST] Substitute equation (2) into equation (1) for d: 2(209 - s) + 6.50s = 836.50 Multiply through to remove the parentheses: 418 - 2s + 6.50s = 836.50 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]: s = [B]93[/B]

A football gained 52 yards during the possession. In the next 3 possessions they gained the same amount of yards each time. If they gained a total of 256 yards, write and solve an equation for how many yards they gained in each of the last 3 possessions. Subtract 52 initial yards 256 - 52 = 204 Now, divide 204 by 3 possessions 204/3 = [B]68 yards[/B]

A football team gained 8 yards on a first down, lost 12 yards on the second down, and gained 16 yards on the third down. How many yards did the team gain or lose? Assumptions: [LIST] [*]We reflect gains by adding [*]We reflect losses by subtracting [/LIST] Plays: [LIST] [*]Gain of 8 = +8 [*]Loss of 12 = -12 [*]Gain of 16 = +16 [/LIST] Net Gain/Loss +8 - 12 + 16 [B]+12 (gain)[/B]

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print. We subtract 5 cm from the length and the width to account for the frame: Unframed Length: 80 - 5 = 75 Unframed Width: 65 - 5 = 60 Area of the unframed rectangle is: A = lw A = 75(60) A = [B]4,500 sq cm[/B]

A gym charges a $30 sign-up fee plus $20 per month. You have a $130 gift card for the gym. When does the total spent on your gym membership exceed the amount of your gift card? Subtract the sign up fee of $30 from your gift card amount: $130 - $30 = $100 Since each month costs $20, we have $100/$20 = 5 months. So if you go for [B]more than 5 months[/B], you'll exceed your gift card.

A hot air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height and let x represent the number of minutes the balloon descends. Descending means we subtract height, so we have: [B]y = 1120 - 80x[/B]

A jet left Nairobi and flew east at an average speed of 231 mph. A passenger plane left four hours later and flew in the same direction but with an average speed of 385 mph. How long did the jet fly before the passenger plane caught up? Jet distance = 231t Passenger plane distance = 385(t - 4) 385(t - 4) = 231t 385t - 1540 = 231t Subtract 231t from each side 154t = 1540 [URL='https://www.mathcelebrity.com/1unk.php?num=154t%3D1540&pl=Solve']Type 154t = 1540[/URL] into the search engine, we get [B]t = 10. [/B] Check our work: Jet distance = 231(10) = 2,310 Passenger plane distance = 385(10 - 4) = 385 * 6 = 2,310

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hours head start. How far from the starting point are the planes? Use the formula D = rt where [LIST] [*]D = distance [*]r = rate [*]t = time [/LIST] The plan traveling 150 mph for 3 hours: Time 1 = 150 Time 2 = 300 Time 3 = 450 Now at Time 3, the other plane starts Time 4 = 600 Time 5 = 750 Time 6 = 450 + 150t = 550t Subtract 150t 400t = 450 Divide each side by 400 t = 1.125 Plug this into either distance equation, and we get: 550(1.125) = [B]618.75 miles[/B]

a landscaper buys 1 gallon of plant fertilizer. he uses 1/5 of the fertilizer, and then divides the rest into 3 smaller bottles. how many gallons does he put into each bottle? First, we find the remaining fraction of fertilizer after using 1/5. [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F5&pl=Subtract']Using our fraction calculator[/URL], we see: 1 - 1/5 = 4/5 To find the amount of fertilizer per bottle, we then [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F5&frac2=3&pl=Divide']divide 4/5 by 3 and we get[/URL]: [B]4/15 gallon per bottle[/B]

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100 Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given: [LIST=1] [*]m = w + 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Rearrange equation 1 in terms of w my subtracting 5 from each side: [LIST=1] [*]w = m - 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Substitute equation (1) and equation (2) into equation (3) 0.5m + m + m - 5 = 100 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get: m = [B]42 [/B] Now, substitute m = 42 into equation 2 to solve for d: d = 0.5(42) d = [B]21 [/B] Now substitute m = 42 into equation 1 to solve for w: w = 42 - 5 w = [B]37 [/B] To summarize our ages: [LIST] [*]Man (m) = 42 years old [*]Daughter (d) = 21 years old [*]Wife (w) = 37 years old [/LIST]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket? Declare variables: [LIST] [*]Let a be the number of adult's tickets [*]Let c be the number of children's tickets [/LIST] Cost = Price * Quantity We're given two equations: [LIST=1] [*]a + c = 20 [*]15a + 10c = 225 [/LIST] Rearrange equation (1) in terms of a: [LIST=1] [*]a = 20 - c [*]15a + 10c = 225 [/LIST] Now that I have equation (1) in terms of a, we can substitute into equation (2) for a: 15(20 - c) + 10c = 225 Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225 We first need to simplify the expression removing parentheses Simplify 15(20 - c): Distribute the 15 to each term in (20-c) 15 * 20 = (15 * 20) = 300 15 * -c = (15 * -1)c = -15c Our Total expanded term is 300-15c Our updated term to work with is 300 - 15c + 10c = 225 We first need to simplify the expression removing parentheses Our updated term to work with is 300 - 15c + 10c = 225 [SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE] (-15 + 10)c = -5c [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -5c + 300 = + 225 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 300 and 225. To do that, we subtract 300 from both sides -5c + 300 - 300 = 225 - 300 [SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE] -5c = -75 [SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE] -5c/-5 = -75/-5 c = [B]15[/B] Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a: a = 20 - 15 a = [B]5[/B]

A man's age (a) 10 years ago is 43 [U]10 years ago means we subtract 10 from a:[/U] a - 10 [U]The word [I]is[/I] means an equation. So we set a - 10 equal to 43 to get our algebraic expression[/U] [B]a - 10 = 43[/B] If the problem asks you to solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=a-10%3D43&pl=Solve']we type this equation into our search engine[/URL] and we get: a = 53

A man's age (a) 10 years ago is 43. Years ago means we subtract [B]a - 10 = 43 [/B] If the problem asks you to solve for a, we type this equation into our math engine and we get: Solve for [I]a[/I] in the equation a - 10 = 43 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 43. To do that, we add 10 to both sides a - 10 + 10 = 43 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] a = [B]53[/B]

a mans age (a) ten years ago The problem asks for an algebraic expression for age. The phrase [I]ago[/I] means before now, so they were younger. And younger means we [B]subtract[/B] from our current age: [B]a - 10[/B]

A man’s age 10 years ago, if he is now n years old. 10 years ago means we subtract from current age: [B]n - 10[/B]

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test? Let's call the 5 point questions m for multiple choice. Let's call the 2 point questions t for true-false. We have two equations: [LIST=1] [*]m + t = 38 [*]5m + 2t = 100 [/LIST] Rearrange (1) to solve for m - subtract t from each side: 3. m = 38 - t Now, substitute (3) into (2) 5(38 - t) + 2t = 100 190 - 5t + 2t = 100 Combine like terms: 190 - 3t = 100 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=190-3t%3D100&pl=Solve']equation solver[/URL], we get [B]t = 30[/B]. Plugging t = 30 into (1), we get: 30 + t = 38 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=m%2B30%3D38&pl=Solve']equation solver[/URL] again, we get [B]m = 8[/B]. Check our work for (1) 8 + 30 = 38 <-- Check Check our work for (2) 5(8) + 2(30) ? 100 40 + 60 ? 100 100 = 100 <-- Check You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+38&term2=5m+%2B+2t+%3D+100&pl=Cramers+Method']simultaneous equations calculator[/URL]

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended. What is the maximum number of events someone can attend for a total cost of $47? Subtract the join fee from the total cost: $47 - $16 = $31 Now divide this number by the cost per event: $31 / $1 = [B]31 events[/B]

A monster energy drink has 164 mg of caffeine. Each hour your system reduces the amount of caffeine by 12%. Write an equation that models the amount of caffeine that remains in your body after you drink an entire monster energy. Set up a function C(h) where he is the number of hours after you drink the Monster energy drink: Since 12% as a decimal is 0.12, we have: C(h) = 164 * (1 - 0.12)^h <-- we subtract 12% since your body flushes it out [B]C(h) = 164 * (0.88)^h[/B]

A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up? In position one, we can have any of the 13 ducks. In position two, we can have 12 ducks, since one has to occupy position one. We subtract 1 each time until we fill up all 13 positions. We have: 13 * 12 * 11 * ... * 2 * 1 Or, 13!. [URL='https://www.mathcelebrity.com/factorial.php?num=13!&pl=Calculate+factorial']Typing 13! into our search engine[/URL], we get [B]6,227,020,800[/B] ways the ducklings can line up behind the mother duck.

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1030, How many children, students, and adults attended? Let c be the number of children's tickets, s be the number of student's tickets, and a be the number of adult's tickets. We have 3 equations: [LIST=1] [*]a + c + s = 143 [*]a = 0.5c [*]12a + 5c + 7s =1030 [/LIST] Substitute (2) into (1) 0.5c + c + s = 143 1.5c + s = 143 Subtract 1.5c from each side 4. s = 143 - 1.5c Now, take (4) and (2), and plug it into (3) 12(0.5c) + 5c + 7(143 - 1.5c) = 1030 6c + 5c + 1001 - 10.5c = 1030 Combine like terms: 0.5c + 1001 = 1030 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.5c%2B1001%3D1030&pl=Solve']equation calculator[/URL] to get [B]c = 58[/B]. Plug this back into (2) a = 0.5(58) [B]a = 29 [/B] Now take the a and c values, and plug it into (1) 29 + 58 + s = 143 s + 87 = 143 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B87%3D143&pl=Solve']equation calculator[/URL] again, we get [B]s = 56[/B]. To summarize, we have: [LIST] [*]29 adults [*]58 children [*]56 students [/LIST]

A non-profit organization is having a couple’s banquet for a fundraiser. The banquet hall will only hold 250 people. The President, Vice-President, two volunteers, and a guest speaker will be working the event. How many couples will be able to attend the banquet? We subtract the 5 people working the event to get: 250 - 5 = 245 A couple is 2 people, so we have 245/2 = 122.5 We round down to [B]122 couples[/B].

A number multiplied by 6 and divided by 5 give four more than a number? A number is represented by an arbitrary variable, let's call it x. Multiply by 6: 6x Divide by 5 6x/5 The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4. 6x/5 = x + 4 Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side: 6x(5)/5 = 5(x + 4) The 5's cancel on the left side, giving us: 6x = 5x + 20 Subtract 5x from each side [B]x = 20[/B] Check our work from our original equation: 6x/5 = x + 4 6(20)/5 ? 20 + 4 120/5 ?24 24 = 24 <-- Yes, we verified our answer

A number n diminished by 8 gives 12 A number n can be written as n: n Diminished by means we subtract, so we subtract 8 from n: n - 8 The word [I]gives[/I] means an equation, so we set n - 8 equal to 12: [B]n - 8 = 12[/B]

A number p subtracted by its double is 10 The double of a number means we multiply p by 2: 2p A number p is subtracted by its double p - 2p The phrase [I]is[/I] means equal to, so we set p - 2p equal to 10: [B]p - 2p = 10[/B]

A parallelogram has a perimeter of 48 millimeters. Two of the sides are each 20 millimeters long. What is the length of each of the other two sides? 2 sides * 20 mm each is 40 mm subtract this from the perimeter of 48: 48 - 40 = 8 Since the remaining two sides equal each other, their length is: 8/2 = [B]4mm[/B]

A parking garage charges $5 plus $2 per hour. You have $16 to spend for parking. How many hours can you park? Subtract the flat rate to get the amount you have for hourly parking: 16 - 5 = 11 So we divide 11 dollars to park by 2 dollars per hour to get: 11/2 [B]5.5 hours[/B]

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of each coin are there? Let d = the number of dimes and q = the number of quarters. We have two equations: (1) d + q = 146 (2) 0.1d + 0.25q = 27.05 Rearrange (1) into (3) solving for d (3) d = 146 - q Substitute (3) into (2) 0.1(146 - q) + 0.25q = 27.05 14.6 - 0.1q + 0.25q = 27.05 Combine q's 0.15q + 14.6 = 27.05 Subtract 14.6 from each side 0.15q = 12.45 Divide each side by 0.15 [B]q = 83[/B] Plugging that into (3), we have: d = 146 - 83 [B]d = 63[/B]

A patient’s temperature was 103°. The temperature then fell by 4° and later rose by 2°. What was the patient’s final temperature Start with 103 Fell by 4 means we subtract 4: 103 - 4 = 99 Rose by 2 means we add 2L 99 + 2 = [B]101[/B]

A person invested 30,000 in stocks and bonds. Her investment in bonds is 2000 more than 1-third her investments in stocks. How much did she invest in stocks? How much did she invest in bonds? Let the stock investment be s, and the bond investment be b. We're given: [LIST=1] [*]b + s = 30000 [*]b = 1/3s + 2000 [/LIST] Plug in (2) to (1): 1/3s + 2000 + s = 30000 Group like terms: (1/3 + 1)s + 2000 = 30000 Since 1 = 3/3, we have: 4/3s + 2000 = 30000 Subtract 2000 from each side: 4/3s + 2000 - 2000 = 30000 - 2000 Cancel the 2000's on the left side, we get: 4/3s = 28000 [URL='https://www.mathcelebrity.com/1unk.php?num=4%2F3s%3D28000&pl=Solve']Typing this equation into our calculator[/URL], we get: s = [B]21,000[/B]

A pet store has 10 rabbits. What’s the probability that they have at least 1 female rabbit. At least 1 female rabbit means we [U]must[/U] have a female rabbit First, we calculate the probability of 0 females A rabbit can be either male or female with equal probabilities of 1/2 or 0.5. Since each birth is independent, we can multiply to get the probability of all males: P(MMMMMMMMMM) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 P(MMMMMMMMMM) = 1/1024 Then, we subtract this probability from 1 to get the probability of [B]at least[/B] one female: P(At least one F) = 1 - 1/1024 Since 1 = 1024/1024, we have: P(At least one F) = (1024 - 1)/1024 P(At least one F) = [B]1023/1024[/B]

A piece of pipe is 144 inches long. After 4 pieces, each 33 inches long are cut, what length of pipe is left? Calculate the length of cut pipe: 4 pieces * 33 inches per piece = 132 inches The remaining pipe is found by subtracting the original pipe length by the cut pipe length: 144 - 132 = [B]12 inches[/B]

A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarters than half dollars, how many of each are there? Let h be the number of half-dollars and q be the number of quarters. Set up two equations: (1) q = h + 2 (2) 0.25q + 0.5h = 11.75 [U]Substitute (1) into (2)[/U] 0.25(h + 2) + 0.5h = 11.75 0.25h + 0.5 + 0.5h = 11.75 [U]Group h terms[/U] 0.75h + 0.5 = 11.75 [U]Subtract 0.5 from each side[/U] 0.75h = 11.25 [U]Divide each side by h[/U] [B]h = 15[/B] [U]Substitute h = 15 into (1)[/U] q = 15 + 2 [B]q = 17[/B]

A private jet flies the same distance in 4 hours that a commercial jet flies in 2 hours. If the speed of the commercial jet was 154 mph less than 3 times the speed of the private jet, find the speed of each jet. Let p = private jet speed and c = commercial jet speed. We have two equations: (1) c = 3p - 154 (2) 4p =2c Plug (1) into (2): 4p = 2(3p - 154) 4p = 6p - 308 Subtract 4p from each side: 2p - 308 = 0 Add 308 to each side: 2p = 308 Divide each side by 2: [B]p = 154[/B] Substitute this into (1) c = 3(154) - 154 c = 462 - 154 [B]c = 308[/B]

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the learners in the class have black hair. How many learners in the class if 9 of them have blonde hair? Total learners = Blond + Brown + Black Total Learners = 1/4 + 2/3 + Black Total Learners will be 1, the sum of all fractions 1/4 + 2/3 + Black = 1 Using common denominators of 12, we have: 3/12 + 8/12 + Black = 12/12 11/12 + Black = 12/12 Subtract 11/12 from each side: Black = 1/12 Let t be the total number of people in class. We are given for blondes: 1/4t = 9 Multiply each side by 4 [B]t = 36[/B] Brown Hair 2/3(36) = 24 Black Hair 1/12(36) = 3

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you get 92. What is the number? Let the rational number be x. We're given: 7x/3 - 3/2 = 92 Using a common denominator of 3*2 = 6, we rewrite this as: 14x/6 - 9/6 = 92 (14x - 9)/6 = 92 Cross multiply: 14x - 9 = 92 * 6 14x - 9 = 552 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=14x-9%3D552&pl=Solve']type this equation into our search engine [/URL]and we get: x = [B]40.07[/B]

A recipe calls for 2 ½ cup of flour, but Paul only has 2 ⅙. How much more flour does he need? Convert to improper fractions [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%261%2F2&frac2=3%2F8&pl=Simplify']2 & 1/2 [/URL]= 5/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%261%2F6&frac2=3%2F8&pl=Simplify']2 & 1/6[/URL] = 13/6 [URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=5%2F2&pl=Equivalent+Fractions']Convert 5/2 to an equivalent fraction with a denominator[/URL] of 6: 15/6 [URL='https://www.mathcelebrity.com/fraction.php?frac1=15%2F6&frac2=13%2F6&pl=Subtract']We subtract 13/6 from 15/6[/URL] 15/6 - 13/6 = 2/6 2/6 = [B]1/3[/B]

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions? We know the rectangle has the following formulas: Area = lw Perimeter = 2l + 2w Given an area of 238 and a perimeter of 62, we have: [LIST=1] [*]lw = 238 [*]2(l + w) = 62 [/LIST] Divide each side of (1) by w: l = 238/w Substitute this into (2): 2(238/w + w) = 62 Divide each side by 2: 238/w + w = 31 Multiply each side by w: 238w/w + w^2 = 31w Simplify: 238 + w^2 = 31w Subtract 31w from each side: w^2 - 31w + 238 = 0 We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get: w = (14, 17) We take the lower amount as our width and the higher amount as our length: [B]w = 14 l = 17 [/B] Check our work for Area: 14(17) = 238 <-- Check Check our work for Perimeter: 2(17 + 14) ? 62 2(31) ? 62 62 = 62 <-- Check

A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions? [LIST=1] [*]Area of a rectangle is lw. lw = 546ft^2 [*]We know that l = w + 5. [/LIST] Substitute (2) into (1) (w + 5)w = 546 w^2 + 5w = 546 Subtract 546 from each side w^2 + 5w - 546 = 0 Using the positive root in our [URL='http://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B5w-546%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get [B]w = 21[/B]. This means l = 21 + 5. [B]l = 26[/B]

a repairman charged $93.06. The price included 2 hours of labor and a $40 service charge. How much does the repairman charge per hour? Subtract the service charge: 93.06 - 40 = 53.06 53.06/2 hours = [B]$26.53 per hour[/B].

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the coaster after the first descent. 90 feet above and then we descend 105 feet, meaning we subtract: 90 - 105 = -15. We read this [B]15 feet below ground level[/B]

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the roller coaster after the first descent. 90 feet above ground level is written as +90 Descending 105 feet means we subtract 105 feet to get: +90 - 105 = [B]-15 or 15 feet below ground level[/B]

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $75. A season ski pass costs $350. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes? Let d be the number of days: Daily Plan cost: 75d + 20d = 95d Season Pass: 350 + 20d We want to find d such that 350 + 20d < 95d Subtract 20d from each side 75d > 350 Divide each side by 75 d > 4.66667 [B]d = 5[/B]

A soft drink costs $1.65, and each refill for the drink costs $0.95. If you have $4.50, how many refills can you purchase? Subtract the first drink: 4.50 - 1.65 = 2.85 Now, we need to find out how many refills we get for 2.85. 2.85/0.95 = [B]3 refills[/B]

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age. Declare variables: [LIST] [*]Let f be the father's age [*]Let s be the son's age [/LIST] We're given two equations: [LIST=1] [*]s = f/4 [*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I] [/LIST] Using substitution, we substitute equaiton (1) into equation (2) for s: f - f/4 = 30 To remove the denominator/fraction, we multiply both sides of the equation by 4: 4f - 4f/4 = 30 *4 4f - f = 120 3f = 120 To solve for f, we divide each side of the equation by 3: 3f/3 = 120/3 Cancel the 3's on the left side and we get: f = [B]40[/B]

A square of an integer is the integer. Find the integer. Let the integer be n. The square means we raise n to the power of 2, so we have: n^2 = n Subtract n from each side: n^2 - n = n - n n^2 - n = 0 Factoring this, we get: n(n - 1) = 0 So n is either [B]0 or 1[/B].

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an item to its list price L. 18% discount means we subtract 18% (0.18) as a decimal, from the 100% of the price: S = L(1 - 0.18) [B]S = 0.82L[/B]

A store manager must calculate the total number of winter hats available to sell in the store from a starting number of 293. In the past month, the store sold 43 blue hats, 96 black hats, 28 red hats, and 61 pink hats. The store received a shipment of 48 blue hats, 60 black hats, 18 red hats, and 24 pink hats. How many total hats does the store have for sale? [LIST=1] [*]We start with 293 hats [*]We calculate the hats sold: (43 + 96 + 28 + 61) = 228 [*]We subtract Step 2 from Step 1 to get remaining hats before the shipment: 293 - 228 = 65 [*]Now we calculate the number of hats received in the shipment: (48 + 60 + 18 + 24) = 150 [*]We add Step 4 to Step 3: 65 + 150 = [B]215 hats for sale[/B] [/LIST]

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 meters, what is its new position? 240 meters below sea level means a negative number, so we start with: -240 Descending 160 meters means our depth decreases, so we subtract: -240 - 160 = -400 Ascends means our depth increases, so we add: -400 + 390 = [B]-10 or 10 feet below sea level [MEDIA=youtube]ngToCpLBgH4[/MEDIA][/B]

A submarine sits at –300 meters in relation to sea level. Then it descends 115 meters. What is its new position in relation to sea level? Descending means we go down in sea level, so we subtract: -300 - 115 = [B]-415 or 415 meters below sea level[/B]

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a. 40 years b. 50 years c. 30 years d. 60 years e. 80 years Simple interest formula if we start with 1 dollar and double to 2 dollars: 1(1 + i(20)) = 2 1 + 20i = 2 Subtract 1 from each side: 20i = 1 Divide each side by 20 i = 0.05 Now setup the same simple interest equation, but instead of 2, we use 3: 1(1 + 0.05(t)) = 3 1 + 0.05t = 3 Subtract 1 from each side: 0.05t = 2 Divide each side by 0.05 [B]t = 40 years[/B]

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take for the tank to be empty Assumptions and givens: [LIST] [*]Let the number of seconds be s. [*]An empty tank means 0 liters of water. [*]Leaks mean we subtract from the starting volume. [/LIST] We have the following relation: 800 - 12s = 0 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=800-12s%3D0&pl=Solve']type it in our search engine[/URL] and we get: s = 66.67 seconds

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? [LIST] [*]Each ride will cost 1.50 + 0.8x where x is the number of miles per trip. [*]This expression must be less than 12. [/LIST] [U]Setup the inequality:[/U] 1.5 + 0.8x < 12 [U]Subtracting 1.5 from each side of the inequality[/U] 0.8x < 10.5 [U]Simplifying even more by dividing each side of the inequality by 0.8, we have:[/U] [B]x < 13.125[/B]

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spend on the cab ride, how far could she travel? Setup an equation where x is the number of miles traveled: 0.65x + 1.75 = 10 Subtract 1.75 from each side: 0.65x = 8.25 Divide each side by 0.65 [B]x = 12.69 miles[/B] If we do full miles, we round down to 12. [MEDIA=youtube]mFqUe2mjX-w[/MEDIA]

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marcos car towed if he received a bill for $71 Set up a cost equation C(m) where m is the number of miles: C(m) = Cost per mile * m + Service Fee Plugging in the service fee of 50 and cost per mile of 1.75, we get: C(m) = 1.75m + 50 The question asks for what m is C(m) = 71. So we set C(m) = 71 and solve for m: 1.75m + 50 = 71 Solve for [I]m[/I] in the equation 1.75m + 50 = 71 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 50 and 71. To do that, we subtract 50 from both sides 1.75m + 50 - 50 = 71 - 50 [SIZE=5][B]Step 2: Cancel 50 on the left side:[/B][/SIZE] 1.75m = 21 [SIZE=5][B]Step 3: Divide each side of the equation by 1.75[/B][/SIZE] 1.75m/1.75 = 21/1.75 m = [B]12[/B]

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continuous at a constant speed of 40 feet per minute for the last 50 feet. (i) Determine which animal won the race. (ii). By how much time the animal won the race. (iii) Explain one life lesson from the race. We know the distance formula is: d = rt For the turtle, he has a rate (r) of 20 feet / minute and distance (d) of 100. We want to solve for time: [URL='https://www.mathcelebrity.com/drt.php?d=+100&r=+20&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get: t = 5 The rabbit has 3 parts of the race: Rabbit Part 1: Distance (d) = 50 and rate (r) = 40 [URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get: t = 1.25 Rabbit Part 2: The rabbit stops for 3 minutes (t = 3) Rabbit Part 3: Distance (d) = 50 and rate (r) = 40 [URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get: t = 1.25 Total time for the rabbit from the 3 parts is (t) = 1.25 + 3 + 1.25 Total time for the rabbit from the 3 parts is (t) = 5.5 [LIST] [*](i) The [B]turtle won[/B] the race because he took more time to finish and they both started at the same time [*](ii) We subtract the turtles time from the rabbit's time: 5.5 - 5 = [B]0.5 minutes which is also 30 seconds[/B] [*](iii) [B]Slow and Steady wins the race[/B] [/LIST]

A TV that usually sells for $192.94 is on sale for 15% off. If sales tax on the TV is 6%, what is the price of the TV, including tax? Find the discounted price: 15% off of 192.94 Discounted Price = 192.94 * (1 - 0.15) <-- 15% as a decimal is 0.15, and 1 is 100%, so we subtract to get 85% of the original price Discounted Price =192.94(0.85) Discounted Price = $164 Now, add in the sales tax of 6% to the Discounted Price Price after sales tax = Discounted Price * 1.06 Price after sales tax = $164 * 1.06 [B]Price after sales tax = $173.84[/B]

a variable tripled less 40 [I]A variable[/I] means we pick an arbitrary variable, let's call it x x Tripled means we multiply by 3 3x Less 40 means we subtract 40: [B]3x - 40[/B]

A+B+D=255 B+15=A D+12=B A= [LIST=1] [*]A + B + D = 255 [*]B + 15 = A [*]D + 12 = B [*]A = ? [*]Rearrange (3) to solve for D by subtracting 12 from each side: D = B - 12 [/LIST] Substitute (2) and (5) into 1 (B + 15) + B + (B - 12) = 255 Combine like terms: 3B + 3 = 255 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3b%2B3%3D255&pl=Solve']equation solver[/URL], b = 84 Substitute b = 84 into equation (2): A = 84 + 15 [B]A = 99[/B]

Multiply through: A = 2l + 2w To solve for l, subtract 2w from each side: 2l = A - 2w Divide each side by 2 l = (A - 2w)/2

Multiply through using the distributive property, so we have: A = 2l + 2w Subtract 2l from each side 2w = A - 2l Divide each side by w w = (A - 2l)/2 [MEDIA=youtube]Nm-tYD4aEY4[/MEDIA]

A=a+b+c+d÷4 for c Assume A and a are different variables: Cross multiply: a + b + c + d = 4A Subtract a, b, and d from each side: a + b + c + d - (a + b + d) = 4A - (a + b + d) Cancel the a + b + d on the left side [B]c = 4A - a - b - d[/B]

Aaron bought a bagel and 3 muffins for $7.25. Bea bought a bagel and 2 muffins for $6. How much is bagel and how much is a muffin? Let b be the number of bagels and m be the number of muffins. We have two equations: [LIST=1] [*]b + 3m = 7.25 [*]b + 2m = 6 [/LIST] Subtract (2) from (1) [B]m = 1.25 [/B] Plug this into (2), we have: b + 2(1.25) = 6 b + 2.5 = 6 Subtract 2.5 from each side [B]b = 3.5[/B]

ab/d + c = e for d I know this is a literal equation because we are asked to solve for a variable [U]in terms of[I] another variable [/I][/U] Subtract c from each side to isolate the d term: ab/d + c - c = e - c Cancel the c's on the left side and we get: ab/d = e - c Cross multiply: ab = d(e - c) Divide each side of the equation by (e - c): ab/(e - c)= d(e - c)/(e - c) Cancel the (e - c) on the right side, and we get: d = [B]ab/(e - c)[/B]

ab/d+c=e for d Subtract c from each side: ab/d+c - c = e - c ab/d = e - c Multiply each side by d: abd/d = d(e - c) ab = d(e - c) Divide each side by (e - c): ab/(e - c) = d(e - c)/(e - c) d =[B] ab/(e - c)[/B]

Free Absolute Value Calculator - Add, subtract, multiply or divide any two numbers with absolute value signs.

acw+cz=y for a Solve this literal equation: Subtract cz from each side: acw + cz - cz = y - cz Cancel the cz on the left side: acw = y - cz Divide each side by cw to isolate a: acw/cw = (y - cz)/cw Cancel cw on the left side: [B]a = (y - cz)/cw[/B]

Adam ate 1/5 of a cake and Matt ate the rest. What fraction did Matt eat? The rest of the cake is 1 - 1/5. 1 as a fraction is 5/5. So we have: 5/5 - 1/5 Using our f[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F5&frac2=1%2F5&pl=Subtract']raction calculator[/URL], we get [B]4/5[/B]

Add 2 and z, then subtract y from the result Add 2 and z 2 + z Subtract y from the result: [B]2 + z - y[/B]

Add 3 to 6, subtract w from the result, then triple what you have Add 3 to 6; 3 + 6 Subtract w from the result; 3 + 6 - w Triple what you have (means multiply by 3): [B]3(3 + 6 - w)[/B]

add c to b, subtract d from the result, then double what you have Add c to b: b + c Subtract d from the result: b + c - d Double what you have means multiply the entire expression by 2: [B]2(b + c - d)[/B]

add d to 5, raise the result to the 9th power, then subtract what you have from 2 Add d to 5: d + 5 Raise the result to the 9th power means we raise (d + 5) to the 9th power using an exponent: (d + 5)^9 the subtract what we have (the result) from 2: [B]2 - (d + 5)^9[/B]

add q and s, subtract r, subtract p Add q and s: q + s Subtract r: q + s - r Subtract p: [B]q + s - r - p[/B]

Add q and t, subtract s from the result, then multiply by r Take this algebraic expression in parts: [LIST] [*]Add q and t: q + t [*]Subtract s from the result: q + t - s [*]Multiply by r means we multiply the entire expression by r: [/LIST] [B]r(q + t - s)[/B]

add r and s, add the result to q, then subtract what you have from p Take this algebraic expression in 3 parts: [LIST=1] [*]Add r and s: r + s [*]Add the result to q: r + s + q [*]Subtract what we have from p: [/LIST] [B]p - (r + s + q)[/B]

add s and 2 then subtract 4 Add s and 2 s + 2 Subtract 4: [B]s + 2 - 4[/B]

add s to r, subtract q from the result Add s to r: r + s Subtract q from the result: [B]r + s - q[/B]

add v to t, add the result to u, then subtract what you have from s Add v to t: t + v Add the result to u: t + v + u Then subtract what you have from s: [B]s - (t + v + u)[/B]

add w and u, subtract t from the result Add w and u: w + u Subtract t from the result: [B]w + u - t[/B]

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair Let the number of students be s and the others be o. We're given two equations: [LIST=1] [*]o + s = 2848 [*]3.75o + 2.50s = 10078.75 [/LIST] Since we have no coefficients for equation 1, let's solve this the fast way using substitution. Rearrange equation 1 by subtracting o from each side to isolate s [LIST=1] [*]o = 2848 - s [*]3.75o + 2.50s = 10078.75 [/LIST] Now substitute equation 1 into equation 2: 3.75(2848 - s) + 2.50s =10078.75 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3.75%282848-s%29%2B2.50s%3D10078.75&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]481[/B]

After buying some tickets for $19.00, Ann has $18.00 left. How much money did Ann have to begin with? Let the beginning amount be b. We're given: b - 19 = 18. <-- [I]We subtract 19 because a purchase is a spend reducing the original amount[/I] To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-19%3D18&pl=Solve']type the equation b - 19 = 18 into our search engine [/URL]and we get: b = [B]37[/B]

Alec had c caramels. Then, Alecs sister took 85 of the caramels. Choose the expression that shows the number of caramels Alec has left. Alec starts with c caramels. His sister took 85. The word [I]took[/I] means subtract, so we have: [B]c - 85[/B]

Alex sells cars at Keith Palmer ford. He earns 400 dollars a week plus 150 dollars per car he sells. If he earned 1450 dollars last week, how many cars did he sell? Subtract the base salary of $400 $1,450 - 400 =$1,050 Divide this by 150 per car $1,050/$150 = [B]7 cars[/B]

Alexandra was given a gift card for a coffee shop. Each morning, Alexandra uses the card to buy one cup of coffee. The original amount of money on the gift card was $45 and each cup of coffee costs $2.50. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee. We start with 45, and each cup of coffee decreases our balance by 2.50, so we subtract: [B]A(x) = 45 - 2.50x[/B]

Alfred carries a load of 12 kilograms. He finds it heavy so he removes a weight of 4 kilograms. What is the weight of the remaining load? Removes means he subtract weight. So we have: 12 kilograms - 4 kilograms = [B]8 kilograms[/B]

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Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account has a balance of $81. How much did she have in her account to start with? We start with a balance of b. Depositing 41 means we add to the account balance: b + 41 Writing checks for 31 and 13 means we subtract from the account balance: b + 41 - 31 - 13 The final balance is 81, so we set b + 41 - 31 - 13 equal to 81: b + 41 - 31 - 13 = 81 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B41-31-13%3D81&pl=Solve']type this equation into our math engine[/URL] and we get: b = [B]84[/B]

Alisha is 5 years younger than her brother. If the age of her brother is y years then age of Alisha in terms of her brother Younger means we subtract. If her brother is y years of age, then Alisha is: [B]y - 5[/B]

Alvin planted t fewer trees than Danielle. Danielle planted 56 trees. Write an expression that shows how many trees Alvin planted. The word [I]fewer[/I] means we subtract, so we have Alvin's tree planting of: [B]56 - t[/B]

An 8 yard gain and a 3 yard loss results in what kind of gain or loss? [LIST=1] [*]Start with 0 yards [*]Gains means we add, so we have 0 + 8 = 8 [*]Losses mean we subtract, so we have 8 - 3 = 5 [/LIST] The overall result is a [B]5 yard gain[/B]

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 1800 feet per minute. Let m be the number of minutes. Which of the following expressions describe the height of the airplane after any given number of minutes? Let m be the number of minutes. Since a descent equals a [U]drop[/U] in altitude, we subtract this in our Altitude function A(m): [B]A(m) = 38,800 - 1800m[/B]

An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and spent the last 13 years as an old man. How old was he when he died? Set up his life equation per time lived as a boy, youth, man, and old man 1/4 + 1/5 + 1/3 + x = 1. Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=5&pl=LCM']LCM Calculator[/URL], we see the LCM of 3,4,5 is 60. This is our common denominator. So we have 15/60 + 12/60 + 20/60 + x/60 = 60/60 [U]Combine like terms[/U] x + 47/60 = 60/60 [U]Subtract 47/60 from each side:[/U] x/60 = 13/60 x = 13 out of the 60 possible years, so he was [B]60 when he died[/B].

An angle is 30 degrees less than 5 times it's complement. Find the angle. Let the angle be a. The complement of a is 90 - a. We're given the following equation: a = 5(90 - a) - 30 <-- Less means we subtract Multiplying though, we get: a = 450 - 5a - 30 a = 420 - 5a [URL='https://www.mathcelebrity.com/1unk.php?num=a%3D420-5a&pl=Solve']Typing this equation into our search engine[/URL], we get: a =[B] 70[/B]

An electrician starts off the day with 600 feet of copper wiring on his truck. During the course of the day he uses pieces 100, 82, 25, and 40 feet long. The next day, he purchases another 400 feet and puts it on his truck and later in the day uses pieces of 41, 39, and 44 feet long. How many feet of wiring are still on the truck at the end of the second day? If the electrician uses pieces, we subtract. If he purchases pieces, we add. So we have: 600 - 100 - 82 - 25 - 40 + 400 - 41 - 39 - 44 = [B]629 feet[/B]

An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How many trees are there in each row? Let the rows be r and the trees per row be t. We're given two equations: [LIST=1] [*]rt = 816 [*]r = t + 10 [/LIST] Substitute equation (2) into equation (1) for r: (t + 10)t = 816 t^2 + 10t = 816 Subtract 816 from each side of the equation: t^2 + 10t - 816 = 816 - 816 t^2 + 10t - 816 = 0 We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B10t-816%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get: t = (24, -34) Since the number of trees per row can't be negative, we choose [B]24[/B] as our answer

An organic juice bottler ideally produces 215,000 bottle per day. But this total can vary by as much as 7,500 bottles. What is the maximum and minimum expected production at the bottling company? Our production amount p is found by adding and subtracting our variance amount: 215,000 - 7,500 <= p <= 215,000 + 7,500 [B](min) 207,500 <= p <=222,500 (max)[/B]

Andrea has one hour to spend training for an upcoming race she completes her training by running full speed in the distance of the race and walking back the same distance to cool down if she runs at a speed of 9 mph and walks back at a speed of 3 mph how long should she plan on spending to walk back Let r = running time. Let w = walking time We're given two equations [LIST=1] [*]r + w = 1 [*]9r = 3w [/LIST] Rearrange equation (1) by subtract r from each side: [LIST=1] [*]w = 1 - r [*]9r = 3w [/LIST] Now substitute equation (1) into equation (2): 9r = 3(1 - r) 9r = 3 - 3r To solve for r, [URL='https://www.mathcelebrity.com/1unk.php?num=9r%3D3-3r&pl=Solve']we type this equation into our search engine[/URL] and we get: r = 0.25 Plug this into modified equation (1) to solve for w, and we get: w = 1. 0.25 [B]w = 0.75[/B]

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at least $100. What is the minimum number of sales you must make to earn at least $100? Set up the inequality where s is the amount of sales you make: 50 + 2s >= 100 We use >= because the phrase [I]at least[/I] 100 means 100 or more Subtract 50 from each side: 2s >= 50 Divide each side by 2 [B]s >= 25[/B]

At a birthday party, 13 children ate cake, 9 ate ice cream, 7 ate both cake and ice cream, and one child had neither cake nor ice cream. How many children were at the party? We have one of three scenarios [LIST=1] [*]A child ate cake (possibly ice-cream) [*]A child ate ice cream (possible cake) [*]A child ate neither [/LIST] We have cake + ice cream + neither - both cake and ice cream. We subtract both cake and ice cream to avoid duplicates 13 + 9 + 1 - 7 = 16 kids at the party

At a local fitness center, members pay a $10 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same? Set up the cost functions where x is the number of aerobics classes: [LIST] [*]Members: C(x) = 10 + 3x [*]Non-members: C(x) = 5x [/LIST] Set them equal to each other 10 + 3x = 5x Subtract 3x from both sides: 2x = 10 Divide each side by 2 [B]x = 5 classes[/B]

At a local fitness center, members pay an $8 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members be equal to nonmembers? Set up two cost equations C(x): [LIST=1] [*]Members: C(x) = 8 + 3x [*]Nonmembers: C(x) = 5x [/LIST] Set the two cost equations equal to each other: 8 + 3x = 5x Subtract 3x from each side 2x = 8 Divide each side by 2 [B]x = 4[/B]

At midnight in Winnipeg, the temperature was −23°C. During the next 24 hours, the temperature rose 12°C, then dropped 8°C. What was the final temperature? We start with −23°C Temperatures rising 12°C mean we add: -23 + 12 = -11 Temperatures dropping 8°C mean we subtract: -11 - 8 = [B]-19°C[/B]

At the beginning of Jack's diet, he was 257 pounds. If he lost 3 pounds per week, find his weight after 12 weeks. A loss of weight means we subtract from Jack's current weight. New Weight = Current Weight - Weight Loss per week * number of weeks New Weight =257 - 3*12 New Weight =257 - 36 New Weight =[B] 221[/B]

At the end of the day, the temperature is -16°C. During the day it dropped 12°C. What was the temperature in the morning? Write an equation to represent, then solve and verify your answer let the starting temperature be s. If the temperature dropped, that means we subtract, so we have the following equation: s - 12 = -16 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=s-12%3D-16&pl=Solve']type it in our search engine[/URL] and we get: s = [B]-4[/B]

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on a movie and popcorn and another $1.35 on a pen. How much did she earn babysitting? Let the original amount of money earned for babysitting be b. We're given: [LIST=1] [*]Start with b [*]Spending 14.65 for a movie means we subtract 14.65 from b: b - 14.65 [*]Spending 1.35 on a pen means we subtract another 1.35 from step 2: b - 14.65 - 1.35 [*]Francesca has a third of her money left. So we set step 3 equal to 1/3 of b [/LIST] b - 14.65 - 1.35 = b/3 Multiply each side of the equation by 3 to remove the fraction 3(b - 14.65 - 1.35) = 3b/3 3b - 43.95 - 4.05 = b To solve this equation for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b-43.95-4.05%3Db&pl=Solve']we type it in our search engine[/URL] and we get: b =[B] 24[/B]

At what simple interest rate will 4500$ amount to 8000$ in 5 years? Simple Interest is written as 1 + it. With t = 5, we have: 4500(1 + 5i) = 8000 Divide each side by 4500 1 + 5i = 1.77777778 Subtract 1 from each side: 5i = 0.77777778 Divide each side by 5 i = 0.15555 As a percentage we multiply by 100 to get [B]15.5%[/B]

Ava set her watch 2 seconds behind, every day it sets back 1 second. How many days has it been since she last set her watch if it is 41 seconds behind? Right now: Watch is 2 seconds behind [U]Let d be the day after right now[/U] (1)d + 2 = 41 d + 2 = 41 [U]Subtract 2 from each side[/U] [B]d = 39[/B]

We are solving for x: Subtract b from each side: ax = cx - d - b Subtract cx from each side: ax - cx = -d - b Factor out x from the left side: x(a - c) = -d - b Divide each side by (a - c) x = (-d - b)/(a - c)

ax - mn = mn + bx for x Add mn to each side: ax - mn + mn = mn + bx + mn Cancel the mn terms on the left side and we get: ax = bx + 2mn Subtract bx from each side: ax - bx = bx - bx + 2mn Cancel the bx terms on the right side: ax - bx = 2mn Factor out x on the left side: x (a - b) = 2mn Divide each side of the equation by (a - b): x (a - b)/(a - b) = 2mn/(a - b) Cancel the (a - b) on the left side and we get: x = [B]2mn/(a - b)[/B]

b is decreased by twice a Twice a means we multiply a by 2: 2a b decreased by twice a means we subtract 2a from b: [B]b - 2a[/B]

b to the fifth power decreased by 7 Take this algebraic expression in steps: [LIST] [*]b to the fifth power: b^5 [*]Decreased by 7 means we subtract 7 from b^5: [B]b^5 - 7[/B] [/LIST]

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Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will it take for them to have the same amount of money? Let w be the number of weeks that go by for saving/spending. Set up Barney's balance equation, B(w). Spending means we [U]subtract[/U] B(w) = Initial Amount - spend per week * w weeks B(w) = 450 - 3w Set up Betty's balance equation, B(w). Saving means we [U]add[/U] B(w) = Initial Amount + savings per week * w weeks B(w) = 120 + 8w The same amount of money means both of their balance equations B(w) are equal. So we set Barney's balance equal to Betty's balance and solve for w: 450 - 3w = 120 + 8w Add 3w to each side to isolate w: 450 - 3w + 3w = 120 + 8w + 3w Cancelling the 3w on the left side, we get: 450 = 120 + 11w Rewrite to have constant on the right side: 11w + 120 = 450 Subtract 120 from each side: 11w + 120 - 120 = 450 - 120 Cancelling the 120's on the left side, we get: 11w = 330 To solve for w, we divide each side by 11 11w/11 = 330/11 Cancelling the 11's on the left side, we get: w = [B]30 [MEDIA=youtube]ifG_q-utgJI[/MEDIA][/B]

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Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation [LIST=1] [*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition. [*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication [/LIST] So we have the start equation: 3x - 7 If the answer was x = -4, then we plug this in to get our number on the right side of the equation: 3(-4) - 7 -12 - 7 -19 This means our original equation was: [B]3x - 7 = -19[/B] And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get: x = -4

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money in terms of the number of quarters and dimes. b)Rearrange the equation to isolate for the number of dimes (D) a) The equation is: [B]0.1d + 0.25q = 4.5[/B] b) Isolate the equation for d. We subtract 0.25q from each side of the equation: 0.1d + 0.25q - 0.25q = 4.5 - 0.25q Cancel the 0.25q on the left side, and we get: 0.1d = 4.5 - 0.25q Divide each side of the equation by 0.1 to isolate d: 0.1d/0.1 = (4.5 - 0.25q)/0.1 d = [B]45 - 2.5q[/B]

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Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admission to the park. Each ride costs $1.50 to ride. Write an inequality to represent the possible number of rides she can ride? First, we subtract the food and admission cost from Beverly's starting balance of $50: Cost available for rides = Starting Balance - Food - Admission Cost available for rides = 50 - 10 - 15 Cost available for rides = 25 Now we set up an inequality for the number of rides (r) that Beverly can ride with the remaining balance: 1.50r <= 25 To solve for r, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.50r%3C%3D25&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get: [B]r <=[/B] [B]16.67[/B]

Bill is q years old. How old will he in 6 years ? How old was he 4 years ago ? Start with q years old. In 6 years means we add since it's the future: [B]q + 6[/B] 4 years ago means we subtract since it's in the past: [B]q - 4[/B]

blair’s bank account was overdrawn by $40. she spent $30 at the grocery store. what is the balance in her account now? The word [I]overdrawn[/I] means a negative balance. So we start with: -40 Spending 30 at the grocery store means we subtract 30 from our initial balance: -40 - 30 = [B]-70 or $70 overdrawn[/B]

Bob bought 10 note books and 4 pens for 18$. Bill bought 6 notebooks and 4 pens for 12$. Find the price of one note book and one pen. Let the price of each notebook be n. Let the price of each pen be p. We're given two equations: [LIST=1] [*]10n + 4p = 18 [*]6n + 4p = 12 [/LIST] Since we have matching coefficients for p, we subtract equation 1 from equation 2: (10 - 6)n + (4 - 4)p = 18 - 12 Simplifying and cancelling, we get: 4n = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=4n%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]n = 1.5[/B] Now, substitute this value for n into equation (2): 6(1.5) + 4p = 12 Multiply through: 9 + 4p = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4p%3D12&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]p = 0.75[/B]

Boris baked 40 cookies. His family ate m of them If his family ate m, that mean we [I]subtract[/I] m from 40. So Boris has the remaining cookies: [B]40 - m[/B]

by + 2/3 = c for y Subtract 2/3 from each side of the literal equation: by + 2/3 - 2/3 = c - 2/3 Cancel the 2/3 on the left side to get: by = c - 2/3 Divide each side by b to isolate y: by/b = (c - 2/3)/b Cancel the b's on the left side to get: y = [B](c - 2/3)/b[/B]

by + 2/3 = c, for y Subtract 2/3 from each side: by = c - 2/3 Divide each side by b y = [B](c - 2/3)/b[/B]

Let f = dollars spent on flights, h dollars spent on hotels, and p dollars spent on all other purchases. [U]Set up our equations:[/U] (1) 4f + 2h + p = 14660 (2) f + h + p = 9480 (3) f = 2h + 140 [U]First, substitute (3) into (2)[/U] (2h + 140) + h + p = 9480 3h + p + 140 = 9480 3h + p = 9340 [U]Subtract 3h to isolate p to form equation (4)[/U] (4) p = 9340 - 3h [U]Take (3) and (4), and substitute into (1)[/U] 4(2h + 140) + 2h + (9340 - h) = 14660 [U]Multiply through[/U] 8h + 560 + 2h + 9340 - 3h = 14660 [U]Combine h terms and constants[/U] (8 + 2 - 3)h + (560 + 9340) = 14660 7h + 9900 = 14660 [U]Subtract 9900 from both sides:[/U] 7h = 4760 [U]Divide each side by 7[/U] [B]h = 680[/B] [U]Substitute h = 680 into equation (3)[/U] f = 2(680) + 140 f = 1360 + 140 [B]f = 1,500[/B] [U] Substitute h = 680 and f = 1500 into equation (2)[/U] 1500 + 680 + p = 9480 p + 2180 = 9480 [U]Subtract 2180 from each side:[/U] [B]p = 7,300[/B]

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax Let the original price be p. p Apply 25% discount first, which is the same as subtracting 0.25: p(1 - 0.25) Subtract 30 for in store buck p(1 - 0.25) - 30 The phrase [I]no more than[/I] means an inequality using less than or equal to: p(1 - 0.25) - 30 <= 60 To solve this inequality for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=p%281-0.25%29-30%3C%3D60&pl=Solve']type it in our math engine[/URL] and we get: [B]p <= 120[/B]

Carter is going away to college and is giving his collection of 531 baseball cards to his cousins. If he gives 227 cards to Lewis, 186 cards to Benny, and 18 cards to Seven, how many cards are left over? When Carter gives away cards, he subtracts from his collection. So we have: 531 - 227 - 186 - 18 = [B]100 cards leftover[/B]

Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her daughter's age Declare variables for each age: [LIST] [*]Let Casey's age be c [*]Let her daughter's age be d [*]Let n be the number of years from now where Casey will be double her daughter's age [/LIST] We're told that: 26 + n = 2(4 + n) 26 + n = 8 + 2n Solve for [I]n[/I] in the equation 26 + n = 8 + 2n [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables n and 2n. To do that, we subtract 2n from both sides n + 26 - 2n = 2n + 8 - 2n [SIZE=5][B]Step 2: Cancel 2n on the right side:[/B][/SIZE] -n + 26 = 8 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 26 and 8. To do that, we subtract 26 from both sides -n + 26 - 26 = 8 - 26 [SIZE=5][B]Step 4: Cancel 26 on the left side:[/B][/SIZE] -n = -18 [SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE] -1n/-1 = -18/-1 n = [B]18[/B] Check our work for n = 18: 26 + 18 ? 8 + 2(18) 44 ? 8 + 36 44 = 44

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them? Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age [LIST=1] [*]a = c + 5 [*]j = a + 6 [*]a + c + j = 31 [*]Rearrange (1) in terms of c: c = a - 5 [/LIST] [U]Plug in (4) and (2) into (3)[/U] a + (a - 5) + (a + 6) = 31 [U]Combine like terms:[/U] 3a + 1 = 31 [U]Subtract 1 from each side[/U] 3a = 30 [U]Divide each side by 3[/U] [B]a = 10[/B] [U]Plug in 1 = 10 into Equation (4)[/U] c = 10 - 5 [B]c = 5[/B] Now plug 1 = 10 into equation (2) j = 10 + 6 [B]j = 16[/B]

Cindy is c years old. Cindy is 5 years younger than half Jennifer's age ( j ) Build an algebraic expression: [B]c = j/2 - 5[/B] <-- Half means we divide by 2 and [I]younger[/I] means we subtract

Class A has 8 pupils and class B has 10 pupils. Both classes sit the same maths test. The mean score for class A is 55. The mean score for both classes is 76. What is the mean score (rounded to 1 DP) in the maths test for class B Mean of the sum equals the sum of the means. U(A + B) = U(A) + U(B) 76 = 55 + U(B) Subtract 55 from each side, we get: [B]U(B) = 21[/B]

Coles paycheck was $257.20. He put 25% of it into his savings account and used 1/3 of what was left to pay bills. How much money does he have remaining from his paycheck? 25% is also 1/4. Calculate savings $257.20(0.25) = $64.3 We have 75% left over = $192.90 Coles pays 1/3 of this for bills = $192.90 * 1/3 = $64.30 Subtract the bills: $192.90 - $64.30 = [B]$128.60[/B]

Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the original number? Let the number be n. Divide by 8: n/8 Then add 1: n/8 + 1 The phrase [I]get an answer[/I] of means an equation, so we set n/8 + 1 equal to 2: n/8 + 1 = 2 To solve for n, we subtract 1 from each side to isolate the n term: n/8 + 1 - 1 = 2 - 1 Cancel the 1's on the left side, we get: n/8 = 1 Cross multiply: n = 8*1 n = [B]8[/B]

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Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve for a, b, or h? Why? Solve for each of these variables to demonstrate. The variable "h" is the easiest to solve for. Because you only have one step. Let's review: Divide each side of the equation by 12(a + b) h = 12(a + b)/A Solving for "a", we two steps. Divide each side by 12h: A/12h = a + b Subtract b from each side a = A/12h - b Solving for "b" takes two steps as well. Divide each side by 12h: A/12h = a + b Subtract a from each side b = A/12h - a

Free Counting on a Number Line Calculator - Shows addition or subtraction by moving left or right on a number line.

cx+b/d=y for b Subtract cx from each side to isolate b/d: cx - cx + b/d = y - cx Cancel the cx terms on each side: b/d = y - cx Cross multiply: b = [B]d(y - cx)[/B]

d is h decreased by 301 h decreased by 301 means we subtract 301 from h h - 301 The phrase [I]is[/I] means equal to, so we set d equal to this expression: [B]d = h - 301[/B]

Dad is (y) years old. Mom is 5 years younger than Dad. What is the total of their ages Dad's age: y Mom's age (younger means we subtract): y - 5 The total of their ages is found by adding them together: y + y - 5 Group like terms, and we get: [B]2y - 5[/B]

Danny's mom ate 1/6 of an ice cream cake. Danny and his sister want to split the remainder of it. How much of the cake would each get? If Danny's mom ate 1/6 of the cake, then we have: 1 - 1/6 of the cake left. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F6&pl=Subtract']use our fraction subtraction calculator[/URL] for 1 - 1/6 to get: 5/6 If Danny and his sister split the remainder, then we divide 5/6 by 2. It's also the same as multiplying 5/6 by 1/2: We [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F6&frac2=1%2F2&pl=Multiply']use our fraction multiplication calculator[/URL] to get: [B]5/12 for Danny and his sister[/B]

Decrease 12 by a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We take 12 and decrease it by x, meaning we subtract x from 12: [B]12 - x[/B]

decrease 19 by c Start with 19 and subtract c: [B]19 - c[/B]

Dennis was getting in shape for a marathon. The first day of the week he ran n miles. Dennis then added a mile to his run each day. By the end of the week (7 days), he had run a total of 70 miles. How many miles did Dennis run the first day? Setup distance ran for the 7 days: [LIST=1] [*]n [*]n + 1 [*]n + 2 [*]n + 3 [*]n + 4 [*]n + 5 [*]n + 6 [/LIST] Add them all up: 7n + 21 = 70 Solve for [I]n[/I] in the equation 7n + 21 = 70 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 21 and 70. To do that, we subtract 21 from both sides 7n + 21 - 21 = 70 - 21 [SIZE=5][B]Step 2: Cancel 21 on the left side:[/B][/SIZE] 7n = 49 [SIZE=5][B]Step 3: Divide each side of the equation by 7[/B][/SIZE] 7n/7 = 49/7 n =[B] 7 [URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B21%3D70&pl=Solve']Source[/URL][/B]

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money? We set up a balance equation B(m) where m is the number of months. [U]Set up Deon's Balance equation:[/U] Withdrawals mean we subtract from our current balance B(m) = Starting Balance - Withdrawal Amount * m B(m) = 650 - 40m [U]Set up Mai's Balance equation:[/U] Withdrawals mean we subtract from our current balance B(m) = Starting Balance - Withdrawal Amount * m B(m) = 850 - 65m When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m: 650 - 40m = 850 - 65m Solve for [I]m[/I] in the equation 650 - 40m = 850 - 65m [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables -40m and -65m. To do that, we add 65m to both sides -40m + 650 + 65m = -65m + 850 + 65m [SIZE=5][B]Step 2: Cancel -65m on the right side:[/B][/SIZE] 25m + 650 = 850 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 650 and 850. To do that, we subtract 650 from both sides 25m + 650 - 650 = 850 - 650 [SIZE=5][B]Step 4: Cancel 650 on the left side:[/B][/SIZE] 25m = 200 [SIZE=5][B]Step 5: Divide each side of the equation by 25[/B][/SIZE] 25m/25 = 200/25 m = [B]8[/B]

Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse any digits. He also only wants an even number that begins with 5. How many possible PINS could he choose from? [LIST=1] [*]First digit must begin with 5. So we have 1 choice [*]We subtract 1 possible digit from digit 3 to have 8 - 1 = 7 possible digits [*]This digit can be anything other than 5 and the even number in the next step. So we have 0-9 is 10 digits - 2 = 8 possible digits [*]Last digit must end in 0, 2, 4, 6, 8 to be even. So we have 5 choices [/LIST] Our total choices from digits 1-4 are found by multiplying each possible digit choice: 1 * 7 * 8 * 5 = [B]280 possible PINS[/B]

Determine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2 For the phrase [I]choose any number[/I] we can use an arbitrary variable, let's call it x. Add 2: x + 2 Multiply your answer to 3: 3(x + 2) And minus 2 which means we subtract: [B]3(x + 2) - 2[/B]

difference between 2 positive numbers is 3 and the sum of their squares is 117 Declare variables for each of the two numbers: [LIST] [*]Let the first variable be x [*]Let the second variable be y [/LIST] We're given 2 equations: [LIST=1] [*]x - y = 3 [*]x^2 + y^2 = 117 [/LIST] Rewrite equation (1) in terms of x by adding y to each side: [LIST=1] [*]x = y + 3 [*]x^2 + y^2 = 117 [/LIST] Substitute equation (1) into equation (2) for x: (y + 3)^2 + y^2 = 117 Evaluate and simplify: y^2 + 3y + 3y + 9 + y^2 = 117 Combine like terms: 2y^2 + 6y + 9 = 117 Subtract 117 from each side: 2y^2 + 6y + 9 - 117 = 117 - 117 2y^2 + 6y - 108 = 0 This is a quadratic equation: Solve the quadratic equation 2y2+6y-108 = 0 With the standard form of ax2 + bx + c, we have our a, b, and c values: a = 2, b = 6, c = -108 Solve the quadratic equation 2y^2 + 6y - 108 = 0 The quadratic formula is denoted below: y = -b ± sqrt(b^2 - 4ac)/2a [U]Step 1 - calculate negative b:[/U] -b = -(6) -b = -6 [U]Step 2 - calculate the discriminant Δ:[/U] Δ = b2 - 4ac: Δ = 62 - 4 x 2 x -108 Δ = 36 - -864 Δ = 900 <--- Discriminant Since Δ is greater than zero, we can expect two real and unequal roots. [U]Step 3 - take the square root of the discriminant Δ:[/U] √Δ = √(900) √Δ = 30 [U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U] Numerator 1 = -b + √Δ Numerator 1 = -6 + 30 Numerator 1 = 24 [U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U] Numerator 2 = -b - √Δ Numerator 2 = -6 - 30 Numerator 2 = -36 [U]Step 6 - calculate your denominator which is 2a:[/U] Denominator = 2 * a Denominator = 2 * 2 Denominator = 4 [U]Step 7 - you have everything you need to solve. Find solutions:[/U] Solution 1 = Numerator 1/Denominator Solution 1 = 24/4 Solution 1 = 6 Solution 2 = Numerator 2/Denominator Solution 2 = -36/4 Solution 2 = -9 [U]As a solution set, our answers would be:[/U] (Solution 1, Solution 2) = (6, -9) Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution

[U]The difference of z and y means we subtract y from z[/U] z - y [U]Now, we form a fraction, where 10 is the numerator and z - y is the denominator[/U] 10/(z - y)

Divide 17 by g. Then, subtract 9. Divide 17 by g 17/g Subtract 9 [B]17/g - 9[/B]

Divide 73 into two parts whose product is 40 Our first part is x Our second part is 73 - x The product of the two parts is: x(73 - x) = 40 Multiplying through, we get: -x^2 + 73x = 402 Subtract 40 from each side, we get: -x^2 + 73x - 402 = 0 This is a quadratic equation. To solve this, we type it in our search engine, choose "solve Quadratic", and we get: [LIST=1] [*]x = [B]6[/B] [*]x = [B]67[/B] [/LIST]

divide 8 by 9, then subtract t Divide 8 by 9 8/9 Then subtract t [B]8/9 - t[/B]

divide a by c, triple the result, then subtract what you have from b Let's take this algebraic expression in parts: [LIST=1] [*]Divide a by c: a/c [*]Triple the result. This means we multiply a/c by 3: 3a/c [*]Then subtract what you have (the result) from b: b - 3a/c [/LIST] [B]b - 3a/c[/B]

divide b by a, subtract the result from c, then add what you have to d Take this algebraic expression in 3 parts: [U]1) Divide b by a:[/U] b/a [U]2) Subtract the result from c:[/U] c - b/a [U]3) Then add what you have to d:[/U] [B]c - b/a + d[/B]

Divide the difference of 4 and r by 10 The difference of 4 and r, mean we subtract r from 4: 4 - r Now we divide this expression by 10: [B](4 - r)/10 [/B]

Divide the sum x and y by the difference of subtracting a from b The sum x and y is written as: x + y The difference of subtracting a from b is written as: b - a We divide and get the algebraic expression: [B](x + y)/(b - a)[/B]

divide u by s, then subtract the result from t Divide u by s: u/s Subtract the result from t: [B]t - u/s[/B]

Do the phrases 7 less than a number and a number less than 7 mean the same thing explain No, they are different, here's how: First, the phrase [I]a number[/I] means an arbitrary variable, let's call it x. 7 less than a number means we subtract 7 from x: x - 7 A number less than 7 means we subtract x from 7: 7 - x As you can see: x - 7 <> 7 - x so [B]they are different[/B]

Dora has $35 saved. She earns $9.50 per hour at her job. How many hours must she work to have a total of $358 in her savings? Subtract the existing savings from the desired savings to see what we have left: 358 - 35 = 323 Now, at 9.50 per hour, how many hours of work does she need to get 323? Let h be the number of hours. We have: 9.50h = 323 [URL='http://www.mathcelebrity.com/1unk.php?num=9.50h%3D323&pl=Solve']Running this problem through our search engine[/URL], we get [B]h = 34[/B]

Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers business cards for $0.15 each with a setup charge of $10. What numbers of business cards cost the same from either company Declare variables: [LIST] [*]Let b be the number of business cards. [/LIST] [U]Set up the cost function C(b) for Dunder Mifflin:[/U] C(b) = Cost to print each business card * b + Setup Charge C(b) = 0.1b + 15 [U]Set up the cost function C(b) for Werham Hogg:[/U] C(b) = Cost to print each business card * b + Setup Charge C(b) = 0.15b + 10 The phrase [I]cost the same[/I] means we set both C(b)'s equal to each other and solve for b: 0.1b + 15 = 0.15b + 10 Solve for [I]b[/I] in the equation 0.1b + 15 = 0.15b + 10 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 0.1b and 0.15b. To do that, we subtract 0.15b from both sides 0.1b + 15 - 0.15b = 0.15b + 10 - 0.15b [SIZE=5][B]Step 2: Cancel 0.15b on the right side:[/B][/SIZE] -0.05b + 15 = 10 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 15 and 10. To do that, we subtract 15 from both sides -0.05b + 15 - 15 = 10 - 15 [SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE] -0.05b = -5 [SIZE=5][B]Step 5: Divide each side of the equation by -0.05[/B][/SIZE] -0.05b/-0.05 = -5/-0.05 b = [B]100[/B]

During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours, t, must you work as a landscaper? [U]Calculate your gas station salary:[/U] Gas Station Salary = Hours Worked * Hourly Rate Gas Station Salary = 30 * $8.75 Gas Station Salary = $262.50 [U]Now subtract this from the desired weekly earnings of $400[/U] $400 - 262.50 = $137.50 The landscaper makes $11 per hour. And they want to make $137.50 from landscaping. So we have the following equation: 11t = 137.50 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=11t%3D137.50&pl=Solve']equation calculator[/URL], and we get t = 12.5 hours.

Dwayne has 9 peppermints. Mary has p fewer peppermints than Dwayne. Choose the expression that shows how many peppermints Mary has. The phrase [I]fewer than[/I] means we subtract: [B]9 - p[/B]

Dylans mother tells Dylan he must spend less time playing electronic games. On the weekends he spends 9.5 hours playing electronic games. If he plays between 13 and 19 hours each week, how many hours does he play games on weekdays? Let x equal the number of hours Dylan plays electronic games per week. [U]Set up our inequality:[/U] 13 <= x <= 19 [U]To see how much he plays during weekdays, subtract off the weekend time[/U] 13 - 9.5 <= x <= 19 - 9.5 [B]3.5 <= x <= 9.5[/B]

Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30. What is the greatest age Mary could be? Let e = Emily's age and m = Mary's age. We have the equation e = 2m + 3 and the inequality e + m < 30 Substitute the equation for e into the inequality: 2m + 3 + m < 30 Add the m terms 3m + 3 < 30 Subtract 3 from each side of the inequality 3m < 27 Divide each side of the inequality by 3 to isolate m m < 9 Therefore, the [B]greatest age[/B] Mary could be is 8, since less than 9 [U]does not include[/U] 9.

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3 times as many 3-cent stamps as 37-cent stamps and half the number of 5-cent stamps as 37-cent stamps. The value of the stamps and coins is $8.28. How many 37-cent stamps does Erin have? Number of stamps: [LIST] [*]Number of 37 cent stamps = s [*]Number of 3-cent stamps = 3s [*]Number of 5-cent stamps = 0.5s [/LIST] Value of stamps and coins: [LIST] [*]37 cent stamps = 0.37s [*]3-cent stamps = 3 * 0.03 = 0.09s [*]5-cent stamps = 0.5 * 0.05s = 0.025s [*]Quarter, 2 dime, 7 pennies = 0.52 [/LIST] Add them up: 0.37s + 0.09s + 0.025s + 0.52 = 8.28 Solve for [I]s[/I] in the equation 0.37s + 0.09s + 0.025s + 0.52 = 8.28 [SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE] (0.37 + 0.09 + 0.025)s = 0.485s [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 0.485s + 0.52 = + 8.28 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 0.52 and 8.28. To do that, we subtract 0.52 from both sides 0.485s + 0.52 - 0.52 = 8.28 - 0.52 [SIZE=5][B]Step 4: Cancel 0.52 on the left side:[/B][/SIZE] 0.485s = 7.76 [SIZE=5][B]Step 5: Divide each side of the equation by 0.485[/B][/SIZE] 0.485s/0.485 = 7.76/0.485 s = [B]16[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=0.37s%2B0.09s%2B0.025s%2B0.52%3D8.28&pl=Solve']Source[/URL]

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept Get this in slope-intercept form by adding 5y to each side: 4x - 5y + 5y = 5y + 20 Cancel the 5y's on the left side and we get: 5y + 20 = 4x Subtract 20 from each side 5y + 20 - 20 = 4x - 20 Cancel the 20's on the left side and we get: 5y = 4x - 20 Divide each side by 5: 5y/5 = 4x/5 - 4 y = 4x/5 - 4 So we have a slope of 4/5 to find our y-intercept, we set x = 0: y = 4(0)/5 - 4 y = 0 - 4 y = -4 If we want a line perpendicular to the line above, our slope will be the negative reciprocal: The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator: m = 5/4 Next, we multiply this by -1: -5/4 So our slope-intercept of the perpendicular line with the same y-intercept is: [B]y = -5x/4 - 4[/B]

ey/n + k = t for y Let's take this literal equation in pieces: Subtract k from each side: ey/n + k - k = t - k Cancel the k's on the left side, we have: ey/n = t - k Now multiply each side by n: ney/n = n(t - k) Cancel the n's on the left side, we have: ey = n(t - k) Divide each side by e: ey/e = n(t - k)/e Cancel the e's on the left side, we have: [B]y = n(t - k)/e[/B]

f+g/e=r for g Subtract f from each side g/e = r - f Multiply each side by e [B]g = e(r - f)[/B]

F/B=(M-N*L)/D for L Cross multiply: DF/B = M - N*L Subtract M from each side: DF/B - M = -N*L Divide each side by -N [B]L = -DF/BN[/B]

Multiply each side by 3 to remove the fraction: 3F=3(2y-z/3) 3F = 6y - z Subtract 6y from each side: 3F - 6y = -z Multiply each side by -1: [B]z = 6y - 3F[/B]

Convert to numbers: Fifteen = 15. Less than means subtract. 3 - 15. Evaluating, that is 12.

fifty feet less means we subtract 50 from 2n. 2n - 50

Find a linear function f, given f(16)=-2 and f(-12)=-9. Then find f(0). We've got 2 points: (16, -2) and (-12, -9) Calculate the slope (m) of this line using: m = (y2 - y1)/(x2 - x1) m = (-9 - -2)/(-12 - 16) m = -7/-28 m = 1/4 The line equation is denoted as: y = mx + b Let's use the first point (x, y) = (16, -2) -2 = 1/4(16) + b -2 = 4 + b Subtract 4 from each side, and we get: b = -6 So our equation of the line is: y = 1/4x - 6 The questions asks for f(0): y = 1/4(0) - 6 y = 0 - 6 [B]y = -6[/B]

So x + y <=18 y = x + 1 x + x + 1 <=18 2x + 1 <= 18 Subtract 1 from both sides 2x <= 17 x<=8.5 --> 8 So we have {(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9)}

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley 216 feet below sea level. Below sea level is the same as being on the opposite side of zero on the number line. To get the difference, we do the following: 1,684 - (-216) Since subtracting a negative is a positive, we have: 1,684 + 216 [B]1,900 feet[/B]

Find two consecutive integers if the sum of their squares is 1513 Let the first integer be n. The next consecutive integer is (n + 1). The sum of their squares is: n^2 + (n + 1)^2 = 1513 n^2 + n^2 + 2n + 1 = 1513 2n^2 + 2n + 1 = 1513 Subtract 1513 from each side: 2n^2 + 2n - 1512 = 0 We have a quadratic equation. We [URL='https://www.mathcelebrity.com/quadratic.php?num=2n%5E2%2B2n-1512%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this into our search engine[/URL] and get: n = (-27, 28) Let's take the positive solution. The second integer is: n + 1 28 + 1 = 29

Find two consecutive positive integers such that the sum of their squares is 25. Let the first integer be x. The next consecutive positive integer is x + 1. The sum of their squares equals 25. We write this as:: x^2 + (x + 1)^2 Expanding, we get: x^2 + x^2 + 2x + 1 = 25 Group like terms: 2x^2 + 2x + 1 = 25 Subtract 25 from each side: 2x^2 + 2x - 24 = 0 Simplify by dividing each side by 2: x^2 + x - 12 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-12%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get x = 3 or x = -4. The problem asks for positive integers, so we discard -4, and use 3. This means, our next positive integer is 3 + 1 = 4. So we have [B](3, 4) [/B]as our answers. Let's check our work: 3^2 + 4^2 = 9 + 16 = 25

Find y if the line through (1,y) and (4,5) has a slope of 3. Slope formula is: m = (y2 - y1)/(x2 - x1) With m = 3, we have: 3 = (5 - y)/(4 - 1) 3 = (5 - y)/3 Cross multiply: 5 - y = 9 Subtract 5 from each side -y = 4 Multiply each side by -1 [B]y = -4[/B]

fixed cost 500 marginal cost 8 item sells for 30. Set up Cost Function C(x) where x is the number of items sold: C(x) = Marginal Cost * x + Fixed Cost C(x) = 8x + 500 Set up Revenue Function R(x) where x is the number of items sold: R(x) = Revenue per item * items sold R(x) = 30x Set up break even function (Cost Equals Revenue) C(x) = R(x) 8x + 500 = 30x Subtract 8x from each side: 22x = 500 Divide each side by 22: x = 22.727272 ~ 23 units for breakeven

Four fifths of s is 4s/5. This is subtracted from 7. 7 - 4s/5

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. 5 times a number: 5x Four less means we subtract 4 from 5x: [B]5x - 4[/B]

Three times y: 3y Four less than three times y means we subtract 4 from3y: [B]3y - 4[/B]

Free Fractions and Mixed Numbers Calculator - Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:
* Addition (Adding)
* Subtraction (Subtracting)
* Positive Difference (Absolute Value of the Difference)
* Multiplication (Multiplying)
* Division (Dividing: complex fraction division is included)
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Fred had 156 dollars to spend on 9 books. After buying them he had 12 dollars. How much did each book cost? Subtract the 12 dollars left over from the $156 starting amount: $156 - $12 = $144 Now divide $144 / 9 books to get the cost per book: $144/9 = [B]$16 per book[/B]

From 199 meters above sea level, Linda took off in her helicopter and descended 296 meters. What is Lindas elevation now? [I]Descended[/I] means we subtract 296 meters from 199 meters. Elevation Now = 199 - 296 Elevation Now = -97 Negative elevation means [I]below sea level[/I]. So our answer is: [B]97 meters [I]below sea level[/I][/B]

FV-O/T=A for o Add O/T to each side: FV-O/T + O/T = A + O/T We have: A + O/T = FV Subtract A from each side: A - A + O/T = FV + A Cancelling the A's, e have: O/T = FV - A Cross multiply the T: [B]O = T(FV - A)[/B]

g equals 232 subtracted from the quantity 377 times g 377 times g: 377g 232 subtracted from 377 times g: 377g - 232 We set the variable g equal to this expression: [B]g = 377g - 232[/B]

g less than 143 is equal to 39 reduced by w g less than 143 means we subtract g from 143 143 - g 39 reduced by w means we subtract w from 39 39 - w We set these 2 expressions equal to each other: [B]143 - g = 39 - w[/B]

Let x equal the number of sticks he started with. We have: The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19 Add 0.2 to each side: 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2 Multiply each side by 5/4 (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24 Multiply the inside piece first: 2/6x - 2/6 - 1/3 2/6x - 4/6 Now subtract 0.75 which is 3/4 2/6x - 4/6 - 3/4 4/6 is 8/12 and 3/4 is 9/12, so we have: 2/6x - 17/12 Now multiply by 3/4 6/24x - 51/48 = 24 Simplify: 1/4x - 17/16 = 24 Multiply through by 4 x - 17/4 = 96 Since 17/4 = 4.25, add 4.25 to each side x = 100.25 Since he did not cut up any sticks, he has a full stick to start with: So x = [B]101[/B]

Given g(a)=a² - 2a - 1 and f(x)=x² - 2x: Find: a) f(a+2) - f(a)/2 b) g(a+h) - g(a)/h a) f(a + 2) = (a + 2)^2 - 2(a + 2) f(a + 2) = a^2 + 2a + 4 - 2a - 4 Simplify and combine like terms: the 2a and 4's cancel, so we have: f(a + 2) = a^2 f(a)/2 = (a^2 - 2a)/2 Subtract one from the other, we get: a^2 - a^2/2 - a [B]a) a^2/2 - a ------------------------[/B] b) g(a + h) = (a + h)^2 - 2(a + h) - 1 g(a + h) = a^2 +2ah + h^2 - 2a - 2h - 1 g(a)/2 = (a^2 - 2a - 1)/h g(a)/2 = (a^2 - 2a - 1)/h Subtract one from the other: g(a+h) - g(a)/h a^2 +2ah + h^2 - 2a - 2h - 1 - (a^2 - 2a - 1)/h Multiply through by h [B]a^2h + 2ah^2 + h^3 - 2ah - 2h^2 - h - a^2 + 2a + 1[/B]

Given: 9 - 4x = -19 Prove: x = 7 Solve for [I]x[/I] in the equation 9 - 4x = - 19 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 9 and -19. To do that, we subtract 9 from both sides -4x + 9 - 9 = -19 - 9 [SIZE=5][B]Step 2: Cancel 9 on the left side:[/B][/SIZE] -4x = -28 [SIZE=5][B]Step 3: Divide each side of the equation by -4[/B][/SIZE] -4x/-4 = -28/-4 x = [B]7[/B]

Given: BC = EF AC = EG AB = 10 BC = 3 Prove FG = 10 [LIST] [*]AC = AB + BC (Segment Addition Postulate) [*]AB = 10, BC = 3 (Given) [*]AC = 10 + 3 (Substitution Property of Equality) [*]AC = 13 (Simplify) [*]AC = EG, BC = EF (Given) [*]EG = 13, EF = 3 (Segment Equivalence) [*]EG = EF + FG (Segment Addition Postulate) [*]13 = 3 + FG (Substitution Property of Equality) [*]FG = 10 (Subtraction Property) [/LIST]

Goal is to take at least 10,000 steps per day. According to your pedometer you have walked 5,274 steps. Write and solve an inequality to find the possible numbers of steps you can take to reach your goal. [U] Subtract off the existing steps (s) from your goal of 10,000[/U] g >= 10000 - 5274 [B]g >= 4726[/B] [I]Note: we use >= since 10,000 steps meets the goal as well as anytihng above it[/I]

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take until they're at the same altitude? Set up the Altitude function A(m) where m is the number of minutes that went by since now. Set up Graham's altitude function A(m): A(m) = 14040 - 50m <-- we subtract for descending Set up Max's altitude function A(m): A(m) = 12500 + 20m <-- we add for ascending Set the altitudes equal to each other to solve for m: 14040 - 50m = 12500 + 20m [URL='https://www.mathcelebrity.com/1unk.php?num=14040-50m%3D12500%2B20m&pl=Solve']We type this equation into our search engine to solve for m[/URL] and we get: m = [B]22[/B]

half of c subtracted from the sum of a and b The sum of a and b: a + b half of c means we divide c by 2: c/2 half of c subtracted from the sum of a and b: [B]a + b - c/2[/B]

half the difference of x and 3 The difference of x and 3 means we subtract 3 from x: x - 3 half of the difference means we divide the difference by 2: [B](x - 3)/2[/B]

Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $2.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours. Happy Paws Cost: C = 16 + 1.5h Woof Watchers: C = 11 + 2.75h Setup the equation where there costs are equal 16 + 1.5h = 11 + 2.75h Subtract 11 from each side: 5 + 1.5h = 2.75h Subtract 1.5h from each side 1.25h = 5 Divide each side by 1.25 [B]h = 4[/B]

How old am I if 400 reduced by 3 times my age is 124? Let my age be a. We're given an algebraic expression: [LIST] [*]3 times my age means we multiply a by 3: 3a [*]400 reduced by 3 times my age means we subtract 3a from 400: [*]400 - 3a [*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124 [/LIST] 400 - 3a = 124 To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get: a = [B]92[/B]

I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 subtract 8. Let the number be n. We're given two equal expressions: [LIST=1] [*]3n + 67 [*]6n - 8 [/LIST] Set the expressions equal to each other since they give the [B]same answer[/B]: 3n + 67 = 6n - 8 We have an equation. [URL='https://www.mathcelebrity.com/1unk.php?num=3n%2B67%3D6n-8&pl=Solve']Type this equation into our search engine and we get[/URL]: n = [B]25[/B]

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13 and subtract 13.What is my number? Take a number (n): The first operation is multiply 5 times n, and then add 39: 5n + 139 The second operation is multiply 13 times n and subtract 13: 13n - 13 Set both operations equal to each other since they result in [I]the same number[/I] 5n + 139 = 13n - 13 [URL='https://www.mathcelebrity.com/1unk.php?num=5n%2B139%3D13n-13&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]n = 19[/B]

I did 4 more problems than Manuel. If I did p problems, write an expression for hw many problems Manuel did. Manuel did 4 less, so we subtract: [B]p - 4[/B]

If $9000 grows to $9720 in 2 years find the simple interest rate. Simple interest formula is Initial Balance * (1 + tn) = Current Balance We have [LIST] [*]Initial Balance = 9000 [*]Current Balance = 9720 [*]n = 2 [/LIST] Plugging in these values, we get: 9000 * (1 + 2t) = 9720 Divide each side by 9000 1 + 2t = 1.08 Subtract 1 from each sdie 2t = 0.08 Divide each side by 2 t = [B]0.04 or 4%[/B]

If 10% of 400 is decreased by 25, the result is? [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=10&den1=400&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']10% of 400 using our search engine[/URL] is 40. The phrase [I]decreased by[/I] means we subtract 25 from 40: 40 - 25 = [B]15[/B]

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions. Convert 2 to a fraction with a denominator of 10: 20/2 = 10, so we multiply 2 by 10/10: 2*10/10 = 20/10 Add 2 to the numerator and denominator: (n + 2)/(d + 2) = 9/10 Cross multiply and simplify: 10(n + 2) = 9(d + 2) 10n + 20 = 9d + 18 Move constants to right side by subtracting 20 from each side and subtracting 9d: 10n - 9d = -2 Subtract 3 from the numerator and denominator: (n - 3)/(d - 3) = 4/5 Cross multiply and simplify: 5(n - 3) = 4(d - 3) 5n - 15 = 4d - 12 Move constants to right side by adding 15 to each side and subtracting 4d: 5n - 4d = 3 Build our system of equations: [LIST=1] [*]10n - 9d = -2 [*]5n - 4d = 3 [/LIST] Multiply equation (2) by -2: [LIST=1] [*]10n - 9d = -2 [*]-10n + 8d = -6 [/LIST] Now add equation (1) to equation (2) (10 -10)n (-9 + 8)d = -2 - 6 The n's cancel, so we have: -d = -8 Multiply through by -1: d = 8 Now bring back our first equation from before, and plug in d = 8 into it to solve for n: 10n - 9d = -2 10n - 9(8) = -2 10n - 72 = -2 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=10n-72%3D-2&pl=Solve']plug this equation into our search engine[/URL] and we get: n = 7 So our fraction, n/d = [B]7/8[/B]

if 2z-1 is an odd integer what is the preceding odd integer? The preceding odd integer is found by subtracting 2: 2z - 1 - 2 [B]2z - 3[/B]

If 2^x + 2^x + 2^x + 2^x = 2^16, what is the value of x? Add up the left side, we get: 4(2^x) = 2^16 But 4 = 2^2, so we have: 2^2(2^x) = 2^16 Using our exponent rule, we have: 2^(x + 2) = 2^16 x + 2 = 16 Subtract 2 from each side, we get: [B]x = 14 [MEDIA=youtube]tm7EyufA6bA[/MEDIA][/B]

If 4x+7=xy-6, then what is the value of x, in terms of y Subtract xy from each side: 4x + 7 - xy = -6 Add 7 to each side: 4x - xy = -6 - 7 4x - xy = -13 Factor out x: x(4 - y) = -13 Divide each side of the equation by (4 - y) [B]x = -13/(4 - y)[/B]

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer. [LIST] [*]Let the integer be "x". [*]Square the integer: x^2 [*]7 times the square: 7x^2 [*]5 times the integer: 5x [*]Add them together: 7x^2 + 5x [*][I]The result is[/I] means an equation, so we set 7x^2 + 5x equal to 2 [/LIST] 7x^2 + 5x = 2 [U]This is a quadratic equation. To get it into standard form, we subtract 2 from each side:[/U] 7x^2 + 5x - 2 = 2 - 2 7x^2 + 5x - 2 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=7x%5E2%2B5x-2%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get two solutions: [LIST=1] [*]x = 2/7 [*]x= -1 [/LIST] The problem asks for an integer, so our answer is x[B] = -1[/B]. [U]Let's check our work by plugging x = -1 into the quadratic:[/U] 7x^2 + 5x - 2 = 0 7(-1)^2 + 5(-1) - 2 ? 0 7(1) - 5 - 2 ? 0 0 = 0 So we verified our answer, [B]x = -1[/B].

If 9/20 of a salad is eaten, how much is leftover? The full salad is 1. Using a common denominator, we have 1 = 20/20 [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=9%2F20&pl=Subtract']So the leftover is 20/20 - 9/20[/URL] = [B]11/20[/B]

If a classroom has 25 students and 8 of them are absent, how many students are present? The word [I]absent[/I] means not in class, so we subtract the 8 absent students from 25 to get: 25 - 8 = [B]17 students present[/B]

If a is an even integer and b is an odd integer then prove a − b is an odd integer Let a be our even integer Let b be our odd integer We can express a = 2x (Standard form for even numbers) for some integer x We can express b = 2y + 1 (Standard form for odd numbers) for some integer y a - b = 2x - (2y + 1) a - b = 2x - 2y - 1 Factor our a 2 from the first two terms: a - b = 2(x - y) - 1 Since x - y is an integer, 2(x- y) is always even. Subtracting 1 makes this an odd number. [MEDIA=youtube]GDVuQ7bGHx8[/MEDIA]

if a number is added to its square, the result is 72. find the number. Let the number be n. We're given: n + n^2 = 72 Subtract 72 from each side, we get: n^2 + n - 72 = 0 This is a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-72%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this equation into our search engine[/URL], and we get: [B]n = 8 and n = -9[/B]

If a number is decreased by 5, and then the result is multiplied by 2, the result is 26 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x [I]Decreased by[/I] means we subtract 5 from x: x - 5 Multiply the result by 2: 2(x - 5) The result is 26 means we set 2(x - 5) equal to 26: [B]2(x - 5) = 26[/B]

If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG? By segment addition, we know that: EF + FG = EG Substituting in our values for the 3 segments, we get: 9x - 17 + 17x - 14 = 20x + 17 Group like terms and simplify: (9 + 17)x + (-17 - 14) = 20x - 17 26x - 31 = 20x - 17 Solve for [I]x[/I] in the equation 26x - 31 = 20x - 17 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides 26x - 31 - 20x = 20x - 17 - 20x [SIZE=5][B]Step 2: Cancel 20x on the right side:[/B][/SIZE] 6x - 31 = -17 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -31 and -17. To do that, we add 31 to both sides 6x - 31 + 31 = -17 + 31 [SIZE=5][B]Step 4: Cancel 31 on the left side:[/B][/SIZE] 6x = 14 [SIZE=5][B]Step 5: Divide each side of the equation by 6[/B][/SIZE] 6x/6 = 14/6 x = [B]2.3333333333333[/B]

If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10 [U]Evaluate f(g(x))[/U] f(g(x)) = 3(x^2 + 2x) + 1 f(g(x)) = 3x^2 + 6x + 1 [U]When f(g(x)) = 10, we have[/U] 10 = 3x^2 + 6x + 1 [U]Subtract 10 from each side:[/U] 3x^2 + 6x - 9 = 0 Divide each side of the equation by 3 x^2 + 2x - 3 = 0 Factor, we have: (x + 3)(x - 1) = 0 So x is either [B]1 or -3[/B]

If f(x) = ax^2 + bx + c and f(0) = 1 and f(-1) = 3, what is a - b Evaluate f(0) f(0) = a(0^2) + b(0) + c f(0) = a(0) + b(0) + c f(0) = c Since f(0) = 1, we have c = 1 Evaluate f(-1) f(-1) = a(-1^2) + b(-1) + c f(-1) = a(1) - b + c f(-1) = a - b + c Since f(-1) = 3, we have: a - b + c = -3 We learned above that f(0) = 1, so c = 1. Plug c = 1 into f(-1) a - b + 1 = -3 Subtract 1 from each side: a - b + 1 - 1 = -3 - 1 Cancel the 1's on the left side and we get: a - b = [B]-4[/B]

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. Twice a number means we multiply x by 2: 2x Subtract four: 2x - 4 The word [I]is [/I]means equal to. We set 2x - 4 equal to 20 for our algebraic expression: [B]2x - 4 = 20 [/B] If the problem asks you to solve for x: we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-4%3D20&pl=Solve']plug this equation into our calculator [/URL]and get x = [B]12[/B]

If i triple the number then subtract 7 the answer is 2. What is the number Let the number be x. Triple the number: 3x Subtract 7 3x - 7 The answer is 2 means we set: [B]3x - 7 = 2[/B] This is our algebraic expression. To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D2&pl=Solve']we type this problem into the search engine[/URL] and get [B]x = 3[/B].

If Jason have 90 pills and have to take 3 pills a day for 3 weeks how many pills do Jason have left? 1 week = 7 days 3 weeks = 7 days * 3 = 21 days 3 pills per day * 21 days = 63 pills Subtract the 63 pills from the 90 pills to get: 90 - 63 = [B]27 pills left[/B]

If Jody had $3 more she would have twice as much as Lars together they have $60. Let j be Jody's money and l be Lars's money. We have two equations: [LIST=1] [*]j + l = 60 [*]j + 3 = 2l [/LIST] Rearrange (2) to solve for j by subtracting 3 j = 2l - 3 Now substitute this into (1) (2l - 3) + l = 60 Combine like terms 3l - 3 = 60 Enter this into our [URL='http://www.mathcelebrity.com/1unk.php?num=3l-3%3D60&pl=Solve']equation calculator[/URL], and we get: [B]l = 21[/B] Now plug l = 21 into our rearranged equation above: j = 2(21) - 3 j = 42 - 3 [B]j = 39[/B]

If n represents an odd integer what represents the previous smaller odd integer Each odd integer is 2 away from the last one, so the previous smaller odd integer is found by subtracting 2 from n: [B]n - 2[/B]

if n(A) = 6, n(A intersect B) = 2 and n(A union B) = 11, find n(B). n(A union B) = n(A) + n(B) - n(A intersect B) Plugging in our given values, we have: 11 = 6 + n(B) - 2 11 = 4 + n(B) Subtract 4 from each side: [B]n(B) = 7[/B]

If p+4=2 and q-3=2, what is the value of qp? Isolate p by subtracting 4 from each side using our [URL='http://www.mathcelebrity.com/1unk.php?num=p%2B4%3D2&pl=Solve']equation calculator[/URL] p = -2 Isolate q by adding 3 to each side using our [URL='http://www.mathcelebrity.com/1unk.php?num=q-3%3D2&pl=Solve']equation calculator[/URL]: q = 5 pq = (-2)(5) [B]pq = -10[/B]

If Susie is 14, what was her age x years ago? x years ago means we subtract x from 14: [B]14 - x[/B]

if the blackout begins at 5:20 pm and ended at 7:05 pm how long did the black out last? [I]add[/I] 2 hours, and we get: 7:20 [I]Subtract[/I] 15 minutes, and we get: 7:05 2 hours - 15 minutes = [B]1 hour and 45 minutes[/B]

Let a be the cost of the ball and b be the cost of the bat: We're given 2 equations: [LIST=1] [*]a + b = 1.10 [*]b = a + 1 [/LIST] Substitute equation (2) into equation (1) for b: a + a + 1 = 1.10 Combine like terms: 2a + 1 = 1.10 Subtract 1 from each side: 2a + 1 - 1 = 1.10 - 1 2a = 0.10 Divide each side by 2: 2a/2 = 0.10/2 a = [B]0.05[/B] [MEDIA=youtube]79q346Hy7R8[/MEDIA]

if the point (.53,y) is on the unit circle in quadrant 1, what is the value of y? Unit circle equation: x^2 + y^2 = 1 Plugging in x = 0.53, we get (0.53)^2 + y^2 = 1 0.2809 + y^2 = 1 Subtract 0.2809 from each side: y^2 = 0.7191 y = [B]0.848[/B]

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially. We know from the distance formula (d) using rate (r) and time (t) that: d = rt Regular speed: 1200 = rt Divide each side by t, we get: r = 1200/t Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3 3600 = (r - 40)(t + 1/3) If we multiply 3 by (t + 1/3), we get: 3t + 1 So we have: 3600 = (r - 40)(3t + 1) Substitute r = 1200/t into the reduced speed equation: 3600 = (1200/t - 40)(3t + 1) Multiply through and we get: 3600 = 3600 - 120t + 1200/t - 40 Subtract 3,600 from each side 3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40 The 3600's cancel, so we get: - 120t + 1200/t - 40 = 0 Multiply each side by t: -120t^2 - 40t + 1200 = 0 We've got a quadratic equation. To solve for t, [URL='https://www.mathcelebrity.com/quadratic.php?num=-120t%5E2-40t%2B1200%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this in our search engine[/URL] and we get: t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is: [B]t = 3[/B]

If the temperature during the day is 6° and the temperature drops 15° after sunset, what is the temperature at night? A drop in temperature means we subtract, so we have: 6 - 15 = [B]-9 or 9 below zero[/B]

If two consecutive even numbers are added, the sum is equal to 226. What is the smaller of the two numbers? Let the smaller number be n. The next consecutive even number is n + 2. Add them together to equal 226: n + n + 2 = 226 Solve for [I]n[/I] in the equation n + n + 2 = 226 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 1)n = 2n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2n + 2 = + 226 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 2 and 226. To do that, we subtract 2 from both sides 2n + 2 - 2 = 226 - 2 [SIZE=5][B]Step 4: Cancel 2 on the left side:[/B][/SIZE] 2n = 224 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2n/2 = 224/2 n = [B]112 [URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B2%3D226&pl=Solve']Source[/URL][/B]

If x2 is added to x, the sum is 42. x^2 + x = 42 Subtract 42 from both sides: x^2 + x - 42 = 0 We have a quadratic equation. Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-42%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation solver[/URL], we get: [B]x = 6 and x = -7 [/B] Since the problem does not state positive number solutions, they are both answers.

If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal installments at 1.73% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid? [U]Determine the monthly payment[/U] The monthly payment is [B]$114.87[/B] using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=3059&av=&pmt=&n=36&i=1.73&check1=1&pl=Calculate']annuity calculator[/URL] [U]Determine the total payments made[/U] Total payment is 36 times $114.87 = $4,135.37 [U]Now determine the total interest paid[/U] Take the total payments of $4,135.37 and subtract the original loan of $3,059 to get interest paid of [B]$1,076.37[/B]

If you divide my brother's age by 3 and then add 20, you will get my age, which is 31. What is my brothers age? Let b be the brother's age. We're given the following relationship for the brother's age and my age: b/3 + 20 = 31 Subtract 20 from each side: b/3 + 20 - 20 = 31 - 20 Cancel the 20's on the left side and we get: b/3 = 11 Cross multiply, and we get: b = 3 * 11 b = [B]33 [/B] Check our work using b = 33 for b/3 + 20 = 31: 33/3 + 20 ? 31 11 + 20 ? 31 31 = 31

If you multiply me by 33 and subtract 20, the result is 46. Who am I? [LIST] [*]Start with the variable x [*]Multiply me by 33 = 33x [*]Subtract 20: 33x - 20 [*]The result is 46, means we set this expression equal to 46: 33x - 20 = 46 [/LIST] Run this through our [URL='http://www.mathcelebrity.com/1unk.php?num=33x-20%3D46&pl=Solve']equation calculator[/URL], and we get: [B]x = 2[/B]

If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you to go 12 miles? (Assume no tip.) a. Create an equation from the information above. b. Identify the slope in the equation? c. Calculate the total cost of the ride? 2. With the same charges as #1, how many miles could you go with $50, if you also gave a $7.50 tip? (Challenge Question! Hint, you only have a $50, exactly, with you a. Cost Equation C(m) for m miles is as follows: [B]C(m) = 1.57m + 5 [/B] b. Slope of the equation is the coefficient for m, which is [B]1.57 [/B] c. Total cost of the ride for m = 12 miles is: C(12) = 1.57(12) + 5 C(12) = 18.84 + 5 C(12) = [B]23.84 [/B] d. If you give a 7.50 tip, we subtract the tip from the $50 to start with a reduced amount: 50 - 7.50 = 42.50 So C(m) = 42.50 1.57m + 5 = 42.50 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.57m%2B5%3D42.50&pl=Solve']type it in our search engine[/URL] and we get: m = 23.89 Since we deal in full miles, we round our answer down to m = [B]23[/B]

If you triple a number and then add 10, you get one-half of the original number. What is the number? Let the number be n. We have: 3n + 10 = 0.5n Subtract 0.5n from each side 2.5n + 10 = 0 Subtract 10 from each side: 2.5n = -10 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2.5n%3D-10&pl=Solve']equation calculator,[/URL] we get: [B]n = -4[/B]

If you triple me, subract 7, and add 4 you get 42. What number am i? Start with an unknown number, "x". Triple me 3x Subtract 7 3x - 7 Add 4 3x - 7 + 4 You get 42 3x - 7 + 4 = 42 Simplify: 3x - 3 = 42 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3x-3%3D42&pl=Solve']equation calculator:[/URL] x = [B]15[/B]

In 16 years, Ben will be 3 times as old as he is right now. Let Ben's age right now be b. We have, in 16 years, Ben's age will be 3 times what his age is now: b + 16 = 3b Subtract b from each side: 2b = 16 Divide each side by 2 [B]b = 8[/B] Check our work: 16 years from now, Ben's age is 8 + 16 = 24 And, 8 x 3 = 24

In 45 years, Gabriela will be 4 times as old as she is right now. Let a be Gabriela's age. we have: a + 45 = 4a Subtract a from each side: 3a = 45 Divide each side by a [B]a = 15[/B]

In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball? Students play either basketball only, baseball only, both sports, or no sports. Let the students who play both sports be b. We have: b + 18 + 7 - 5 = 26 <-- [I]We subtract 5 because we don't want to double count the students who played a sport who were counted already [/I] We [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B18%2B7-5%3D26&pl=Solve']type this equation into our search engine[/URL] and get: b = [B]6[/B]

In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class? We start by declaring variables for boys and girls: [LIST] [*]Let b be the number of boys [*]Let g be the number of girls [/LIST] We're given two equations: [LIST=1] [*]b = g + 5 [*]b + g = 13 [/LIST] Substitute equation (1) for b into equation (2): g + 5 + g = 13 Grouping like terms, we get: 2g + 5 = 13 Subtract 5 from each side: 2g + 5 - 5 = 13 - 5 Cancel the 5's on the left side and we get: 2g = 8 Divide each side of the equation by 2 to isolate g: 2g/2 = 8/2 Cancel the 2's on the left side and we get: g = 4 Substitute g = 4 into equation (1) to solve for b: b = 4 + 5 b = [B]9[/B]

In a golf tournament Ned was 4 under par on Saturday and 5 over or on Sunday. What is the difference in his score on Sunday compared to his score on Saturday Givens and opening thoughts: [LIST] [*]Think of par as 0 or average. [*]Under par is negative [*]Over par is positive [*]We have 4 under par as -4 [*]We have 5 over par as +5 [/LIST] The difference is found by subtracting: +5 - -4 +5 + 4 [B]9 strokes[/B]

In a shipment of 330 animals, 125 were hogs, 68 were sheep, and the rest were cattle. Find the number of cattle in the shipment. To find the rest (cattle), we subtract off the hogs and sheep from the total. Cattle = Total Animals - Hogs - Sheep Cattle = 330 - 125 - 68 [B]Cattle = 137[/B]

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? Let w be the winning team's points, and l be the losing team's points. We have two equations: [LIST=1] [*]w + l = 41 [*]w - l = 27 [/LIST] Add the two equations: 2w = 68 Divide each side by 2 [B]w = 34[/B] Substitute this into (1) 34 + l = 41 Subtract 34 from each side [B]l = 7[/B] Check your work: [LIST=1] [*]34 + 7 = 41 <-- check [*]34 - 7 = 27 <-- check [/LIST] The final score of the game was [B]34 to 7[/B]. You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=w+%2B+l+%3D+41&term2=w+-+l+%3D+27&pl=Cramers+Method']simultaneous equation solver[/URL].

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year Let the starting book count be b. We have: [LIST] [*]We start with b books [*]Buying 237 books means we add (+237) [*]Removing 67 books means we subtract (-67) [*]We end up with 5745 books [/LIST] Our change during the year is found by the equation: b + 237 - 67 = 5745 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B237-67%3D5745&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]5575[/B]

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 Ric, Nancy, and Michael ages added up to 78 years. How old was Ric in 1980? Age in 1980: [LIST] [*]Let Michael's age be m [*]Nancy's age is 2m [*]Rick's age is 2 * 2m = 4m [/LIST] Age in 1992: [LIST] [*]Michael's age = m + 12 [*]Nancy's age is 2m + 12 [*]Rick's age is 2 * 2m = 4m + 12 [/LIST] Total them up: m + 12 + 2m + 12 + 4m + 12 = 78 Solve for [I]m[/I] in the equation m + 12 + 2m + 12 + 4m + 12 = 78 [SIZE=5][B]Step 1: Group the m terms on the left hand side:[/B][/SIZE] (1 + 2 + 4)m = 7m [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 12 + 12 + 12 = 36 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 7m + 36 = + 78 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants 36 and 78. To do that, we subtract 36 from both sides 7m + 36 - 36 = 78 - 36 [SIZE=5][B]Step 5: Cancel 36 on the left side:[/B][/SIZE] 7m = 42 [SIZE=5][B]Step 6: Divide each side of the equation by 7[/B][/SIZE] 7m/7 = 42/7 m = 6 Rick's age = 6 * 4 = [B]24 [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B12%2B2m%2B12%2B4m%2B12%3D78&pl=Solve']Source[/URL] [/B]

In x years time, Peter will be 23 years old. How old is he now? Let Peter's current age be a. In x years time means we add x to a, so we're given: a + x = 23 We want to find a, s we subtract x from each side to get: a + x - x = 23 - x Cancel the x terms on the left side and we get: a = [B]23 - x[/B]

Ina has $40 in her bank account and saves $8 a week. Ree has $200 in her bank account and spends $12 a week. Write an equation to represent each girl. Let w equal the number of weeks, and f(w) be the amount of money in the account after w weeks: [LIST] [*]Ina: [B]f(w) = 40 + 8w[/B] [LIST] [*]We add because Ina saves money, so her account grows [/LIST] [*]Ree: [B]f(w) = 200 - 12w[/B] [LIST] [*]We subtract because Ree saves [/LIST] [/LIST]

Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible numbers of additional minutes she will run? Set up our inequality. If she ran 22 minutes, we need to find an expression to find out the remaining minutes x + 22 < 36 Subtract 22 from each side: x < 14 Remember, she cannot run negative minutes, so our lower bound is 0, so we have: [B]0 < x < 14 [/B]

j - m/4 = 4k for m Multiply each side by 4: 4j - 4m/4 = 4(4k) Simplify: 4j - m = 16k Add m to each side: 4j - m + m = 16k + m The m's cancel on the left side, so we have: 4j = 16k + m Subtract 16k from each side: 4j - 16k = 16k - 16k + m The 16k cancels on the right side, so we're left with: [B]m = 4j - 16k or 4(j - 4k)[/B]

Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Jack spent $40 for the tickets Let a = Number of adult tickets and c be the number of child tickets. [LIST=1] [*]7a + 4c = 40 [*]a + c = 7 [*]Rearrange (2): a = 7 - c [/LIST] Now substitute a in (3) into (1): 7(7 - c) + 4c = 40 49 - 7c + 4c = 40 49 - 3c = 40 Add 3c to each side and subtract 40: 3c = 9 Divide each side by 3: [B]c = 3 [/B] Substitute c = 3 into Equation (2) a + 3 = 7 Subtract 3 from each side: [B]a = 4[/B]

James is ordering action figures online. Each action figure is $9. Shipping cost $10 per order. James does not want to spend over $154. How many action figures can he order? Step 1: Subtract the cost of shipping from the spend $154 - $10 = $144 Step 2: Divide $144 to spend after shipping by $9 action figures 144/9 = [B]$16 action figures[/B]

Jane did this calculation a. Add -12 b.subtract -9 c. Add 8 d. Subtract -2 the result is -5. What was the original number? Let the original number be n. [LIST=1] [*]Add -12: n - 12 [*]Subtract -9: n - 12 - -9 = n - 12 + 9 [*]Add 8: n - 12 + 9 + 8 [*]Subtract - 2: n - 12 + 9 + 8 - -2 = n - 12 + 9 + 8 + 2 [*]The result is -5. So we build the following equation: [/LIST] n - 12 + 9 + 8 + 2 = -5 To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-12%2B9%2B8%2B2%3D-5&pl=Solve']type it in our search engine[/URL] and we get: [B]n = -12[/B]

Jane has $7.50 to spend in the candy store. She likes lollipops and gumballs. Each lollipop costs $2.75, and each gumball costs $0.50. If Jane decides to buy 1 lollipop, then what is the greatest number of gumballs Jane can buy? A Subtract the cost of 1 lollipop: $7.50 - $2.75 = $4.75 Let the number of gumballs = g. We have: 0.50g = $4.75 [URL='https://www.mathcelebrity.com/1unk.php?num=0.50g%3D4.75&pl=Solve']Run this through the search engine[/URL] to get g = 9.5 The problem asks for the greatest number. So we round down to [B]9 gumballs[/B].

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an inequality to show how many sodas he can buy. Let s be the number of sodas. Cost for the day is: Price per soda * s + Admission Price 4.25s + 42 We're told that Jane has 55, which means Jane cannot spend more than 55. Jane can spend up to or less than 55. We write this as an inequality using <= 55 [B]4.25s + 42 <= 55[/B] [B][/B] If the problems asks you to solve for s, we type it in our math engine and we get: Solve for [I]s[/I] in the inequality 4.25s + 42 ≤ 55 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 42 and 55. To do that, we subtract 42 from both sides 4.25s + 42 - 42 ≤ 55 - 42 [SIZE=5][B]Step 2: Cancel 42 on the left side:[/B][/SIZE] 4.25s ≤ 13 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.25[/B][/SIZE] 4.25s/4.25 ≤ 13/4.25 [B]s ≤ 3.06[/B]

Jane received 183 more votes than jack. If jack received n votes, how many votes did Jane receive? Let j = jane's votes. We have, j + 183 = n Subtract 183 from each side: j = n - 183

[SIZE=6]Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 miles per hour. How long does it take Joe to catch Jason? A. 3 hours B. 4 hours C. 6 hours D. 8 hours Distance formula is d = rt Jason's formula (Add 9 since he's ahead 9 miles): d = 5.5t + 9 Joe's formula: d = 7t Set both distance formulas equal to each other: 5.5t + 9 = 7t Subtract 5.5t from each side: 5.5t - 5.5t + 9 = 7t - 5.5t 1.5t = 9 Divide each side by 1.5: 1.5t/1.5 = 9/1.5 t = [B]6 hours[/B] [U]Check our work with t = 6[/U] Joe = 7(6) = 42 Jason = 5.5(6) + 9= 33 + 9 = 42 [MEDIA=youtube]qae3WCq9wzM[/MEDIA] [/SIZE]

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many weeks will Jenny and Kelsey have the same amount of money? Jenny: Let w be the number of weeks. Spending means we subtract, so we set up a balance equation B(w): B(w) = 1200 - 40w Kelsey: Let w be the number of weeks. Saving means we add, so we set up a balance equation B(w): B(w) = 120 + 50w When they have the same amount of money, we set the balance equations equal to each other: 1200 - 40w = 120 + 50w To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-40w%3D120%2B50w&pl=Solve']type this equation into our search engine[/URL] and we get: w = [B]12[/B]

Jenny has $40 in her checking account. If she writes a check for $19 find her new account balance Writing a check means we take out of the account, so we subtract: Balance = $40 - $19 Balance = [B]$21[/B]

Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. How many pairs does Jenny have and how many pairs does her brother have? [U]Let j be the number of shoes Jenny has and b be the number of s hoes her brother has. Set up 2 equations:[/U] (1) b + j = 25 (2) j = b + 5 [U]Substitute (2) into (1)[/U] b + (b + 5) = 25 [U]Group the b terms[/U] 2b + 5 = 25 [U]Subtract 5 from each side[/U] 2b = 20 [U]Divide each side by b[/U] [B]b = 10 [/B] [U]Substitute b = 10 into (2)[/U] j = 10 + 5 [B]j = 15[/B]

Jill made 122 muffins. She put them into 3 boxes and has two muffins left. How many are in each box if they all contain the same amount of muffins? Let m equal the number of muffins per box. We're told that we have 3 boxes and 2 muffins left after filling up all 3 boxes. 3m + 2 = 122 To solve for m, we subtract 2 from each side: 3m + 2 - 2 = 122 - 2 Cancel the 2's on the left side and we get: 3m = 120 Divide each side by 3 to isolate m: 3m/3 = 120/3 Cancel the 3's on the left side and we get: m = [B]40[/B]

Jim was thinking of a number. Jim adds 20 to it, then doubles it and gets an answer of 99.2. What was the original number? Start with x. Add 20 to it x + 20 Double it 2(x + 20) Set this equal to 99.2 2(x + 20) = 99.2 Divide each side by 2: x + 20 = 49.6 Subtract 20 from each side: x = [B]29.6[/B]

Joaquin buys 3 dozen lightbulbs. After changing the lightbulbs in his house,he has 15 lightbulbs left. How many lightbulbs did he use? [URL='https://www.mathcelebrity.com/quantcon.php?quant=3&pl=Calculate&type=dozen']Type 3 dozen into the search engine[/URL]. We get 36 units. Now, if Joaquin has 15 lightbulbs left, we subtract 15 from 36: 36 - 15 = [B]21 lightbulbs used[/B]

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different account that starts with $1000 but withdraws $15 each week. When will Joe and Bria have the same amount of money? Let w be the number of weeks. Deposits mean we add money and withdrawals mean we subtract money. [U]Joe's Balance function B(w) where w is the number of weeks:[/U] 20 + 10w [U]Bria's Balance function B(w) where w is the number of weeks:[/U] 1000 - 15w [U]The problem asks for when both balances will be the same. So we set them equal to each other and solve for w:[/U] 20 + 10w = 1000 - 15w To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=20%2B10w%3D1000-15w&pl=Solve']type this equation into our search engine[/URL] and we get: w = 39.2 We round up to full week and get: w = [B]40[/B]

Joelle had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost? Subtract the $10 left over from the $24 Joelle started with. $24 - $10 = $14 Therefore, Joelle spent $14 on seven pencils. Cost per pencil = Total Pencil Spend / Number of pencils Cost per pencil = 14 / 7 Cost per pencil = [B]$2[/B]

John Adams was born in 1732 and became president in 1797. Harry S. Truman was born in 1884 and became President in 1945. Who was older when he became president? Adams: [URL='http://www.mathcelebrity.com/longdiv.php?num1=1797&num2=1732&pl=Subtract']1797 - 1732[/URL] = 65 Truman: [URL='http://www.mathcelebrity.com/longdiv.php?num1=1945&num2=1884&pl=Subtract']1945 - 1884[/URL] = 61 Adams was older.

John is n years old now. How old was he 10 years ago? What will be his age in 20 years time? 10 years ago means we [I]subtract[/I] 10 from n: [B]n - 10[/B] 20 years time or 20 years from now means we [I]add[/I] 20 to n: [B]n + 20[/B]

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month? [U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 10% written as a decimal is 0.1. We want decimals to solve equations easier. S(m) = 0.1m + 1500 [U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 15% written as a decimal is 0.15. We want decimals to solve equations easier. S(m) = 0.15m + 1200 [U]The question asks what is m when both S(m)'s equal each other[/U]: The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other 0.1m + 1500 = 0.15m + 1200 We want to isolate m terms on one side of the equation. Subtract 1200 from each side: 0.1m + 1500 - 1200 = 0.15m + 1200 - 1200 Cancel the 1200's on the right side and we get: 0.1m - 300 = 0.15m Next, we subtract 0.1m from each side of the equation to isolate m 0.1m - 0.1m + 300 = 0.15m - 0.1m Cancel the 0.1m terms on the left side and we get: 300 = 0.05m Flip the statement since it's an equal sign to get the variable on the left side: 0.05m = 300 To solve for m, we divide each side of the equation by 0.05: 0.05m/0.05 = 300/0.05 Cancelling the 0.05 on the left side, we get: m = [B]6000[/B]

Jose bought 2 movie tickets and a box of popcorn. The popcorn cost $6, and he spent a total of $24. How much did each ticket cost? Subtract the cost of the popcorn: $24 - $6 = $18 2 movie tickets cost $18, so each movie ticket cost $18/2 = [B]$9[/B]

Jose earned 60 points on a game show. In the next round he lost 64 points then gained 12 points and at last lost 28 points. What was his score at the end of the show? Start with 60 points: 60 lose 64 means we subtract 64 from our points 60 - 64 = -4 Gained 12 means we add 12 to our points: -4 + 12 = 8 Lost 28 means we subtract 28 from our points: 8 - 28 = [B]-20 points[/B]

Juan spent at most $2.50 on apples and oranges. He bought 5 apples at $0.36 each. What is the most he spent on oranges? Let a be spending apples and o be spending on oranges, we have: [LIST=1] [*]a + o <= 2.36 <-- At most means less than or equal to [*]a = 5 * 0.36 = 1.8 [/LIST] Substitute (2) into (1) 1.8 + o <= 2.36 Subtract 1.8 from each side [B]o <= 0.56[/B]

Julie has $48 to spend at a carnival. The carnival charges $8 for admission and $5 per ride. What is the maximum number of rides Julie can go on? Subtract admission charges, since that money is gone: $48 - $8 = $40 left over If rides cost $5, we can go on $40/$5 = [B]8 rides[/B] maximum.

Julio had $20 in his account. He made two withdrawals of $15 and $25, and then he deposits $28. What is his account balance now? Note: Balances add and Withdrawals subtract. So we have: 20 - 15 - 25 + 28 [B]8[/B]

k add 2 multiply by 6 then subtract 8 k add 2: k + 2 Multiply by 6: 6(k + 2) Then subtract 8: [B]6(k + 2) - 8[/B]

k add d , multiply by e , then subtract f . [LIST] [*]k add d: k + d [*]Multiply by e: e(k + d) [*]Then subtract f: [B]e(k + d) - f[/B] [/LIST]

Karmen just got hired to work at Walmart. She spent $15 on her new uniform and she gets paid $8 per hour. Write an equation that represents how much money she profits after working for a certain number of hours. How many hours will she have to work for in order to buy a new snowboard ( which costs $450) Her profit equation P(h) where h is the number of hours worked is: [B]P(h) = 8h - 15[/B] Note: [I]We subtract 15 as the cost of Karmen's uniform. [/I] Next, we want to see how many hours Karmen must work to buy a new snowboard which costs $450. We set the profit equation equal to $450 8h - 15 = 450 [URL='https://www.mathcelebrity.com/1unk.php?num=8h-15%3D450&pl=Solve']Typing 8h - 15 = 450 into the search engine[/URL], we get h = 58.13. We round this up to 59 hours.

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat? Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given: [LIST=1] [*]4s + p = 11.45 [*]5s + 3p + c = 27.41 [*]5s + c = 16.94 [/LIST] Rearrange (1) by subtracting 4s from each side: p = 11.45 - 4s Rearrange (3)by subtracting 5s from each side: c = 16.94 - 5s Take those rearranged equations, and plug them into (2): 5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41 Multiply through: 5s + 34.35 - 12s + 16.94 - 5s = 27.41 [URL='https://www.mathcelebrity.com/1unk.php?num=5s%2B34.35-12s%2B16.94-5s%3D27.41&pl=Solve']Group like terms using our equation calculator [/URL]and we get: [B]s = 1.99 [/B] <-- Shirt Cost Plug s = 1.99 into modified equation (1): p = 11.45 - 4(1.99) p = 11.45 - 7.96 [B]p = 3.49[/B] <-- Slacks Cost Plug s = 1.99 into modified equation (3): c = 16.94 - 5(1.99) c = 16.94 - 9.95 [B]c = 6.99[/B] <-- Sports Coat cost

Giving away 2 means subtracting, so we have 10 - 2 = 8 pens left over.

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive? Let t = number of 20 bills and f = number of 50 bills. We have two equations. (1) 20t + 50f = 390 (2) t + f = 15 [U]Rearrange (2) into (3) for t, by subtracting f from each side:[/U] (3) t = 15 - f [U]Now substitute (3) into (1)[/U] 20(15 - f) + 50f = 390 300 - 20f + 50f = 390 [U]Combine f terms[/U] 300 + 30f = 390 [U]Subtract 300 from each side[/U] 30f = 90 [U]Divide each side by 30[/U] [B]f = 3[/B] [U]Substitute f = 3 into (3)[/U] t = 15 - 3 [B]t = 12[/B]

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type? Let d be dimes and q be quarters. Set up two equations from our givens: [LIST=1] [*]d + q = 41 [*]0.1d + 0.25q = 7.85 [/LIST] [U]Rearrange (1) by subtracting q from each side:[/U] (3) d = 41 - q [U]Now, substitute (3) into (2)[/U] 0.1(41 - q) + 0.25q = 7.85 4.1 - 0.1q + 0.25q = 7.85 [U]Combine q terms[/U] 0.15q + 4.1 = 7.85 [U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.15q%2B4.1%3D7.85&pl=Solve']equation calculator[/URL], we get:[/U] [B]q = 25[/B] [U]Substitute q = 25 into (3)[/U] d = 41 - 25 [B]d = 16[/B]

Kevin is 4 times old as Daniel and is also 6 years older than Daniel. Let k be Kevin's age and d be Daniel's age. We have 2 equations: [LIST=1] [*]k = 4d [*]k = d + 6 [/LIST] Plug (1) into (2): 4d = d + 6 Subtract d from each side: 4d - d = d - d + 6 Cancel the d terms on the right side and simplify: 3d = 6 Divide each side by 3: 3d/3 = 6/3 Cancel the 3 on the left side: d = 2 Plug this back into equation (1): k = 4(2) k = 8 So Daniel is 2 years old and Kevin is 8 years old

Kierra had $35 to spend at the movies. If it was $11 to get in and snacks were 2$ each, how many snacks could she buy? Subtract off cover charge: 35 - 11 = 24 Let s equal the number of snacks Kierra can buy. With each snack costing $2, we have the following equation: 2s = 24 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2s%3D24&pl=Solve']equation calculator[/URL], we have: [B]s = 12[/B]

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test This is a missing average problem. Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60? [SIZE=5][B]Setup Average Equation:[/B][/SIZE] Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers 60 = (68 + 72 + x)/3 [SIZE=5][B]Cross Multiply[/B][/SIZE] 68 + 72 + x = 60 x 3 x + 140 = 180 [SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE] x + 140 - 140 = 180 - 140 x = [B]40[/B]

kira will spend less than 27 on gifts. so far, she has spent 12$. what are the possible additional amounts she will spend? The key word in this problem is [I]less than[/I]. So we know this is an inequality. Let s be Kira's possible spend. We have: s + 12 < 27 To solve for s in this inequality, we subtract 12 from each side: s + 12 - 12 < 27 - 12 Cancel the 12's on the left side, and we get: [B]s < 15 [/B] [I]The summary here is Kira can spend anything up to [U]but not including[/U] 15[/I]

larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers Declare Variables for each number: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 12 [*]l + s = 74 [/LIST] Equation (1) already has l solved for. Substitute equation (1) into equation (2) for l: s + 12 + s = 74 Solve for [I]s[/I] in the equation s + 12 + s = 74 [SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE] (1 + 1)s = 2s [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2s + 12 = + 74 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 12 and 74. To do that, we subtract 12 from both sides 2s + 12 - 12 = 74 - 12 [SIZE=5][B]Step 4: Cancel 12 on the left side:[/B][/SIZE] 2s = 62 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2s/2 = 62/2 s = [B]31[/B] To solve for l, we substitute in s = 31 into equation (1): l = 31 + 12 l = [B]43[/B]

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number? Declare variables for the 2 numbers: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 4 [*]l + s = 40 [/LIST] To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l. Subtract 4 from each side in equation (1) l - 4 = s + 4 - 4 Cancel the 4's and we get: s = l - 4 Our given equations are now: [LIST=1] [*]s = l - 4 [*]l + s = 40 [/LIST] Substitute equation (1) into equation (2) for s: l + l - 4 = 40 Grouping like terms for l, we get: 2l - 4 = 40 Add 4 to each side: 2l - 4 + 4 = 40 + 4 Cancelling the 4's on the left side, we get 2l = 44 Divide each side of the equation by 2 to isolate l: 2l/2 = 44/2 Cancel the 2's on the left side and we get: l = [B]22[/B]

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate. Let x be the amount invested at 6%. Then 31000 - x is invested at 7%. We have the following equation: 0.06x + (31000 - x)0.07 = 2090 Simplify: 0.06x + 2170 - 0.07x = 2090 Combine like Terms -0.01x + 2170 = 2090 Subtract 2170 from each side -0.01x = -80 Divide each side by -0.01 x = [B]8000 [/B]at 6% Which means at 7%, we have: 31000 - 8000 = [B]23,000[/B]

Laura weighs 45 pounds more than her pet dog. When they are on the scale together, they weigh 85 pounds. How much does Laura weigh? Let Laura weigh l and her dog weigh d. WE have: [LIST=1] [*]l = d + 45 [*]d + l = 85 [/LIST] Substitute equation (1) into Equation (2) for l: d + d + 45 = 85 Solve for [I]d[/I] in the equation d + d + 45 = 85 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (1 + 1)d = 2d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2d + 45 = + 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 45 and 85. To do that, we subtract 45 from both sides 2d + 45 - 45 = 85 - 45 [SIZE=5][B]Step 4: Cancel 45 on the left side:[/B][/SIZE] 2d = 40 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2d/2 = 40/2 d = 20 From equation (1), we substitute d = 20: l = d + 45 l = 20 + 45 l = [B]65 pounds [URL='https://www.mathcelebrity.com/1unk.php?num=d%2Bd%2B45%3D85&pl=Solve']Source[/URL][/B]

Lei is 15 years old, represent her age m years ago years ago means we subtract: [B]15 - m[/B]

Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What could N be? Is there more than one answer? For example, for 23 P(23) = 6 and S(23) = 5, but 23 could not be the N that we want since 23 <> 5 + 6 Let t = tens digit and o = ones digit P(n) = to S(n) = t + o P(n) + S(n) = to + t + o N = 10t + o Set them equal to each other N = P(N) + S(N) 10t + o = to + t + o o's cancel, so we have 10t = to + t Subtract t from each side, we have 9t = to Divide each side by t o = 9 So any two-digit number with 9 as the ones digit will work: [B]{19,29,39,49,59,69,79,89,99}[/B]

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes. If the total value of the coins is 2.18, how many of each denomination does she have? [U]Set up two equations where p is the number of pennies and d is the number of dimes:[/U] (1) d + p = 47 (2) 0.1d + 0.01p = 2.18 [U]Rearrange (1) into (3) by solving for d[/U] (3) d = 47 - p [U]Substitute (3) into (2)[/U] 0.1(47 - p) + 0.01p = 2.18 4.7 - 0.1p + 0.01p = 2.18 [U]Group p terms[/U] 4.7 - 0.09p = 2.18 [U]Add 0.09p to both sides[/U] 0.09p + 2.18 = 4.7 [U]Subtract 2.18 from both sides[/U] 0.09p = 2.52 [U]Divide each side by 0.09[/U] [B]p = 28[/B] [U]Now substitute that back into (3)[/U] d =47 - 28 [B]d = 19[/B]

Look at this sequence: 53, 53, 40, 40, 27, 27, ... What number should come next? This looks like a sequence where we subtract 13 and then 0, 13 and then 0 from the prior number. Since the last group of 27 repeated, our next number is found by subtracting 13: 27 - 13 = [B]14[/B]

Louis kept money through a hole inn his pocket. He started with 35 cents, lost 20 cents , put in 75 cents , spent 43 cents, lost 16 cents again, and then put in 14 cents. How much change should there be in his pocket? The phrase [I]put in[/I] mean we add money to the total The phrases s[I]pent or lost[/I] mean we subtract 35 - 20 + 75 - 43 - 16 + 14 = [B]45 cents[/B]

Maria bought 7 boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start? [U]Let x be the starting box number. We have:[/U] (x + 7)/2 = 22 [U]Cross multiply[/U] x + 7 = 44 [U]Subtract 7 from each side[/U] [B]x = 37[/B]

Let n be the number of nickels and q be the number of quarters. We have two equations: (1) n + q = 24 (2) 0.05n + 0.25q = 3 Rearrange (1) to solve for n in terms of q for another equation (3) (3) n = 24 - q Plug (3) into (2) 0.05(24 - q) + 0.25q = 3 Multiply through: 1.2 - 0.05q + 0.25q = 3 Combine q terms 0.2q + 1.2 = 3 Subtract 1.2 from each side: 0.2q = 1.8 Divide each side by 0.2 [B]q = 9[/B]

Mary is x years old. How old will she be in 9 years? How old was she 8 years ago In 9 years, we add, since her age goes up, so she'll be: [B]x + 9 [/B] 8 years ago, we subtract, since her age goes down, so she'll be: [B][B]x - 8[/B][/B]

Do we have to subtract out the space covered by the house?

[QUOTE="math_celebrity, post: 1046, member: 1"]Do we have to subtract out the space covered by the house?[/QUOTE] I think so

Matilda needs at least $112 to buy an new dress. She has already saved $40. She earns $9 an hour babysitting. Write and solve and inequality to find how many hours she will need to babysit to buy the dress. Subtract remaining amount needed after savings: 112 - 40 = 72 Let h be her hourly wages for babysitting. We have the equation: [B]9h = 72[/B] Divide each side by 9 [B]h = 8[/B]

Matthew's cat weighs 10 pounds more than his pet hamster. His dog weighs the same as his cat. If the weight of all three pets is 35 pounds, ow much does his hamster weigh? Setup weights and relations: [LIST] [*]Hamster weight: w [*]Cat weight: w + 10 [*]Dog weight:w + 10 [/LIST] Add all the weights up: w + w + 10 + w + 10 = 35 Solve for [I]w[/I] in the equation w + w + 10 + w + 10 = 35 [SIZE=5][B]Step 1: Group the w terms on the left hand side:[/B][/SIZE] (1 + 1 + 1)w = 3w [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 10 + 10 = 20 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 3w + 20 = + 35 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants 20 and 35. To do that, we subtract 20 from both sides 3w + 20 - 20 = 35 - 20 [SIZE=5][B]Step 5: Cancel 20 on the left side:[/B][/SIZE] 3w = 15 [SIZE=5][B]Step 6: Divide each side of the equation by 3[/B][/SIZE] 3w/3 = 15/3 w =[B] 5[/B] [B] [URL='https://www.mathcelebrity.com/1unk.php?num=w%2Bw%2B10%2Bw%2B10%3D35&pl=Solve']Source[/URL][/B]

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00. Bob bought 3 burgers and 1 drink for $5.50. How much is each burger and drink? [U]Set up the givens where b is the cost of a burger and d is the cost of a drink:[/U] Max: 2b + 2d = 5 Bob: 3b + d = 5.50 [U]Rearrange Bob's equation by subtracting 3b from each side[/U] (3) d = 5.50 - 3b [U]Now substitute that d equation back into Max's Equation[/U] 2b + 2(5.50 - 3b) = 5 2b + 11 - 6b = 5 [U]Combine b terms:[/U] -4b + 11 = 5 [U]Subtract 11 from each side[/U] -4b = -6 [U]Divide each side by -4[/U] b = 3/2 [B]b = $1.50[/B] [U]Now plug that back into equation (3):[/U] d = 5.50 - 3(1.50) d = 5.50 - 4.50 [B]d = $1.00[/B]

Michael invited 30 of his friends to his part and a third of guest arrived late how many arrived on time If 1/3 arrived late, then [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F3&pl=Subtract']1 - 1/3[/URL] = 2/3 arrived on time Guests who arrived on time = 2/3 of 30 [URL='https://www.mathcelebrity.com/fraction.php?frac1=30&frac2=2/3&pl=Multiply']Guests who arrived on time[/URL] = [B]20[/B]

Michelle and Julie sold 65 cupcakes. If Julie sold 9 more cupcakes than Michelle, how many cupcakes did each of them sell? Let m = Michelle's cupcakes and j = Julie's cupcakes. We have two equations: m + j = 65 j = m + 9 Substituting, we get: m + (m + 9) = 65 Combine like terms, we get: 2m + 9 = 65 Subtract 9 from each side: 2m = 56 Divide each side by 2 to isolate m m = 28 If m = 28, then j = 28 + 9 = 37 So (m, j) = (28, 37)

Mimis math class starts at 9:00 A.M. and lasts for 1 hour and 55 minutes. After math class, Mimi has recess for 15 minutes. What time does Mimis recess end? [LIST=1] [*]Start at 9:00 AM [*]1 hour and 55 minutes of class puts us at 10:55 AM [*]Recess for 15 minutes puts us at [B]11:10 AM[/B] [/LIST] [B][/B] [LIST=1] [*]Another way to do this is work in whole hours and minute blocks [*]9:00 AM, add 1 hour that is 10:00 AM [*]55 minutes is 5 minutes less than 1 hour [*]So add another hour to 10:00 AM which is 11:00 AM [*]Subtract the 5 minutes is 10:55 AM [*]15 minutes is 5 minutes + 10 minutes [*]Add 5 minutes to 10:55AM is 11:00 [*]10 minutes added to this is [B]11:10 AM[/B] [/LIST]

Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake and troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake (c) that were in total Let c be the total number of pieces of cake. Let m be the number of pieces Mindy ate. Let t be the number of pieces Troy ate. We have the following given equations: [LIST] [*]m + t = 9 [*]m = 3 [*]t = 1/4c [/LIST] Combining (2) and (3) into (1), we have: 3 + 1/4c = 9 Subtract 3 from each side: 1/4c = 6 Cross multiply: [B]c = 24 [MEDIA=youtube]aeqWQXr5f_Y[/MEDIA][/B]

Mr. Smith wants to spend less than $125 at a zoo. A ticket cost $7 he is taking 2 kids with him. Use p to represent the other money he can spend there. 2 kids and Mr. Smith = 3 people. Total Ticket Cost is 3 people * 7 per ticket = 21 If he has 125 to spend, we have the following inequality using less than or equal to (<=) since he can spend up to or less than 125: p + 21 <= 125 Subtract 21 from each side: [B]p <= 104[/B]

Mr. Winkle downloaded 34 more songs than Mrs. Winkle downloaded. Together they downloaded 220 songs. How many songs did each download? Let x = Mr. Winkle downloads and y = Mrs. Winkle downloads. We then have x = y + 34 and x + y = 220. Substitute equation 1 into equation 2, we have: (y + 34) + y = 220 2y + 34 = 220 Subtract 34 from each side: 2y = 186 Divide each side by 2: y = 93 (Mrs. Winkle) x = 93 + 34 x = 127 (Mr. Winkle)

Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest and the middle son gets $35 more than the youngest, how much does each boy get? Let 0 be the oldest son, m be the middle sun, and y be the youngest son. Set up our given equations [LIST] [*]o = 2y [*]m = y + 35 [*]o + m + y = 975 [/LIST] [U]Substitute the first and second equations into Equation 3[/U] 2y + y + 35 + y = 975 [U]Combine the y terms[/U] 4y + 35 = 975 Subtract 35 using our [URL='http://www.mathcelebrity.com/1unk.php?num=4y%2B35%3D975&pl=Solve']equation calculator[/URL] to solve and get [B]y = 235[/B] [U]Plug y = 235 into equation 2[/U] m = 235 + 35 [B]m = 270[/B] [U]Plug y = 235 into equation 2[/U] o = 2(235) [B]o = 470[/B]

multiply 3 by the difference of u and t Take this algebraic expression in parts: The difference of u and t means we subtract t from u u - t Multiply this difference by 3: [B]3(u - t)[/B]

multiply 9 by 3, subtract y from the result Multiply 9 by 3 9 * 3 Subtract y from the result [B]9 * 3 - y[/B]

multiply a number by 4 and then subtract the answer from 30 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x Multiply this number by 4: 4x Subtract the answer from 30: [B]30 - 4x[/B]

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and subtracting 4. Find the number The phrase [I]a number [/I]means an arbitrary variable, let's call it x. multiply a number by 6 and subtract 6: 6x - 6 Multiply a number by 3 and subtract 4: 3x - 4 The phrase [I]gives the same result[/I] means an equation. So we set 6x - 6 equal to 3x - 4 6x - 6 = 3x - 4 To solve this equation for x, we type it in our search engine and we get: x = [B]2/3[/B]

multiply k by 5.8, and then subtract 3.09 from the product Take this algebraic expression in pieces: [U]Multiply k by 5.8:[/U] 5.8k [U]Then subtract 3.09 from the product[/U] [B]5.8k - 3.09[/B]

Multiply the difference of 3 and q by p. Take this algebraic expression in pieces: [B][U]Step 1: The difference of 3 and q[/U][/B] The word [I]difference[/I] means we subtract the variable q from 3 3 - q [B][U]Step 2: Multiply the expression 3 - q by p:[/U] p(3 - q)[/B]

n + 9n - 8 - 5 = 2n + 3 Solve for [I]n[/I] in the equation n + 9n - 8 - 5 = 2n + 3 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 9)n = 10n [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] -8 - 5 = -13 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 10n - 13 = 2n + 3 [SIZE=5][B]Step 4: Group variables:[/B][/SIZE] We need to group our variables 10n and 2n. To do that, we subtract 2n from both sides 10n - 13 - 2n = 2n + 3 - 2n [SIZE=5][B]Step 5: Cancel 2n on the right side:[/B][/SIZE] 8n - 13 = 3 [SIZE=5][B]Step 6: Group constants:[/B][/SIZE] We need to group our constants -13 and 3. To do that, we add 13 to both sides 8n - 13 + 13 = 3 + 13 [SIZE=5][B]Step 7: Cancel 13 on the left side:[/B][/SIZE] 8n = 16 [SIZE=5][B]Step 8: Divide each side of the equation by 8[/B][/SIZE] 8n/8 = 16/8 n = [B]2[/B]

n = 3n - 1/2 Solve for [I]n[/I] in the equation n = 3n - 1/2 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables n and 3n. To do that, we subtract 3n from both sides n - 3n = 3n - 0.5 - 3n [SIZE=5][B]Step 2: Cancel 3n on the right side:[/B][/SIZE] -2n = -0.5 [SIZE=5][B]Step 3: Divide each side of the equation by -2[/B][/SIZE] -2n/-2 = -0.5/-2 n = [B]0.25 or 1/4[/B]

n = b + d^2a for a Let's start by isolating the one term with the a variable. Subtract b from each side: n - b = b - b + d^2a Cancel the b terms on the right side and we get: n - b = d^2a With the a term isolated, let's divide each side of the equation by d^2: (n - b)/d^2 = d^2a/d^2 Cancel the d^2 on the right side, and we'll display this with the variable to solve on the left side: a = [B](n - b)/d^2 [MEDIA=youtube]BCEVsZmoKoQ[/MEDIA][/B]

n is tripled then decreased by 5 n is tripled means we multiply n by 3: 3n Decreased by 5 means we subtract 5 from 3n: [B]3n - 5[/B]

N reduced by 2 is the same as Z increased by 7 [LIST] [*]N reduced by 2 means subtract --> n - 2 [*]z increased by 7 means add --> z + 7 [*][I]Is the same as[/I] means equal to, so we set these expressions equal to each other [*][B]n - 2 = z + 7[/B] [/LIST]

N squared multiplied by the difference of n and 3 n squared means we raise n to the power of 2: n^2 The difference of n and 3 means we subtract 3 from n: n - 3 Now we multiply both terms together: [B]n^2(n - 3)[/B]

n subtract m, multiply by c, then add w Take this algebraic expression in pieces: [LIST] [*]n subtract m: n - m [*]multiply by c: c(n - m) [*]Then add w: [B]c(n - m) + w[/B] [/LIST]

n=i*x+y for i This is a literal equation. Subtract y from each side of the equation: n - y = i*x + y - y The y's cancel on the right side, so we have: n - y = ix Divide each side of the equation by x, to isolate i (n - y)/x = ix/x The x's cancel on the right side, so we have: i = [B](n - y)/x[/B]

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. [I]When will they both have the same amount of money in the bank?[/I] [I][/I] Set up the Account equation A(w) where w is the number of weeks that pass. Nancy (we add since savings means she accumulates [B]more[/B]): A(w) = 25w + 435 Shane (we subtract since spending means he loses [B]more[/B]): A(w) = 875 - 15w Set both A(w) equations equal to each other to since we want to see what w is when the account are equal: 25w + 435 = 875 - 15w [URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B435%3D875-15w&pl=Solve']Type this equation into our search engine to solve for w[/URL] and we get: w =[B] 11[/B]

Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that shows how much money Nick has after x amount of days. Set up the function M(x) where M(x) is the amount of money after x days. Since spending means a decrease, we subtract to get: [B]M(x) = 50 - 5x[/B]

The product of 2 and y means we multiply 2y Nine less than that product means we subtract 9 2y - 9 Finally, the entire expression is not less than 15, which means 15 or more. We use greater than or equal to [B]2y - 9 >= 15 [/B] If you want to solve this inequality and write the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=2y-9%3E%3D15&pl=Solve']our calculator[/URL].

less than means we subtract 9 from 12: [B]12 - 9[/B] <-- This is our algebraic expression IF we want to evaluate this, it's: 12- 9 = [B]3[/B]

Free Number Bonds Calculator - Adds or subtracts 2 numbers and using grouping by 10 or 100. Also called number bonds or addition facts. Multiplies two numbers using tape diagrams.

n^2 + 9 = 34 Subtract 9 from each side: n^2 + 9 - 9 = 34 - 9 n^2 = 25 Take the square root of each side: n = [B]5[/B]

On a farm, the farmer harvested 34.7 crates of apples and 25.9 crates of oranges. How much more crates of apples are harvested? How much more means we subtract: 34.7 - 25.9 = [B]8.8 more craters of apples[/B]

On July 10, the high temperature in Phoenix, Arizona, was 109°, and the high temperature in Juneau, Alaska, was 63°. What was the difference between the temperature in Phoenix and the temperature in Juneau? Difference is found by subtracting the lower temperature from the higher temperature: [URL='https://www.mathcelebrity.com/longdiv.php?num1=109&num2=63&pl=Subtract']109 - 63 [/URL]= [B]46[/B]

One and one-third can be written as 4/3. Less x means minus x, or subtract x. 4/3 - x Or in mixed number notation: 1 & 1/3 - x

One number is equal to the square of another. Find the numbers if both are positive and their sum is 650 Let the number be n. Then the square is n^2. We're given: n^2 + n = 650 Subtract 650 from each side: n^2 + n - 650 = 0 We have a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-650%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this into our search engine[/URL] and we get: n = 25 and n = -26 Since the equation asks for a positive solution, we use [B]n = 25[/B] as our first solution. the second solution is 25^2 = [B]625[/B]

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. One-third a number means we multiply x by 1/3: x/3 Less two means we subtract 2 [B]x/3 - 2[/B]

Out of 53 teachers 36 drink tea 18 drink coffee, 10 drink neither. how many drink both? Let T be tea drinkers Let C be coffee drinkers Let (T & C) be Tea & Coffee drinkers. And 53 are total. So we use the Union formula relation: C U T = C + T - (C & T) 53 = 18 + 36 - (C & T) C & T = 53 - (Not C & Not T) since we subtract people who don't drink coffee and don't drink tea C & T = 53 - 10 = 43 C U T = 18 + 36 - 43 C U T = [B]11[/B]

Subtract 15 from each side: 5d/11 = P - 15 Multiply each side by 11 5d = 11p - 165 Divide each side of the equation by d: d = (11p - 165) ------------ 5

Patricia has $425.82 in her checking account. How much does she have in her account after she makes a deposit of $120.75 and a withdrawal of $185.90? Start with $425.82 Deposits mean we [B]add[/B] money to the bank account: 425.82 + 120.75 = 546.57 Our new balance is 546.57. Withdrawals mean we [B]subtract[/B] money from the bank account: 546.57 - 185.90 = [B]360.67[/B]

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Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width? The perimeter P of a rectangle with length l and width w is: 2l + 2w = P We're given P = 372 and l = 99, so we have: 2(99) + 2w = 372 2w + 198 = 372 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 198 and 372. To do that, we subtract 198 from both sides 2w + 198 - 198 = 372 - 198 [SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE] 2w = 174 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 174/2 w = [B]87[/B]

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200? Set P(t) = 19,200 0.7t^2+6t+15,000 = 19,200 Subtract 19,200 from each side: 0.7t^2+6t+4200 = 0 The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B] t 0.7t^2 6t Add 15000 Total 1 0.7 6 15000 15006.7 2 2.8 12 15000 15014.8 3 6.3 18 15000 15024.3 4 11.2 24 15000 15035.2 5 17.5 30 15000 15047.5 6 25.2 36 15000 15061.2 7 34.3 42 15000 15076.3 8 44.8 48 15000 15092.8 9 56.7 54 15000 15110.7 10 70 60 15000 15130 11 84.7 66 15000 15150.7 12 100.8 72 15000 15172.8 13 118.3 78 15000 15196.3 14 137.2 84 15000 15221.2 15 157.5 90 15000 15247.5 16 179.2 96 15000 15275.2 17 202.3 102 15000 15304.3 18 226.8 108 15000 15334.8 19 252.7 114 15000 15366.7 20 280 120 15000 15400 21 308.7 126 15000 15434.7 22 338.8 132 15000 15470.8 23 370.3 138 15000 15508.3 24 403.2 144 15000 15547.2 25 437.5 150 15000 15587.5 26 473.2 156 15000 15629.2 27 510.3 162 15000 15672.3 28 548.8 168 15000 15716.8 29 588.7 174 15000 15762.7 30 630 180 15000 15810 31 672.7 186 15000 15858.7 32 716.8 192 15000 15908.8 33 762.3 198 15000 15960.3 34 809.2 204 15000 16013.2 35 857.5 210 15000 16067.5 36 907.2 216 15000 16123.2 37 958.3 222 15000 16180.3 38 1010.8 228 15000 16238.8 39 1064.7 234 15000 16298.7 40 1120 240 15000 16360 41 1176.7 246 15000 16422.7 42 1234.8 252 15000 16486.8 43 1294.3 258 15000 16552.3 44 1355.2 264 15000 16619.2 45 1417.5 270 15000 16687.5 46 1481.2 276 15000 16757.2 47 1546.3 282 15000 16828.3 48 1612.8 288 15000 16900.8 49 1680.7 294 15000 16974.7 50 1750 300 15000 17050 51 1820.7 306 15000 17126.7 52 1892.8 312 15000 17204.8 53 1966.3 318 15000 17284.3 54 2041.2 324 15000 17365.2 55 2117.5 330 15000 17447.5 56 2195.2 336 15000 17531.2 57 2274.3 342 15000 17616.3 58 2354.8 348 15000 17702.8 59 2436.7 354 15000 17790.7 60 2520 360 15000 17880 61 2604.7 366 15000 17970.7 62 2690.8 372 15000 18062.8 63 2778.3 378 15000 18156.3 64 2867.2 384 15000 18251.2 65 2957.5 390 15000 18347.5 66 3049.2 396 15000 18445.2 67 3142.3 402 15000 18544.3 68 3236.8 408 15000 18644.8 69 3332.7 414 15000 18746.7 70 3430 420 15000 18850 71 3528.7 426 15000 18954.7 72 3628.8 432 15000 19060.8 73 3730.3 438 15000 19168.3 74 3833.2 444 15000 19277.2

Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7. Collinear means on the same line. By segment subtraction, we have: AB = AC - BC AB = 15 - 7 AB = [B]8[/B]

Prove P(A’) = 1 - P(A) The sample space S contains an Event A and everything not A, called A' We know P(S) = 1 P(S) = P(A U A') P(A U A') = 1 P(A) + P(A') = 1 subtract P(A) from each side: P(A’) = 1 - P(A) [MEDIA=youtube]dNLl_8vejyE[/MEDIA]

Take an integer n. The next alternate consecutive integer is n + 2 Subtract the difference of the squares: (n + 2)^2 - n^2 n^2 + 4n + 4 - n^2 n^2 terms cancel, we get: 4n + 4 Factor out a 4: 4(n + 1) If n is odd, n + 1 is even. 4 * even is always even If n is even, n + 1 is odd. 4 * odd is always odd Since both cases are even, we've proven our statement. [MEDIA=youtube]J_E9lR5qFY0[/MEDIA]

Take an integer n. The next consecutive integer is n + 1 Subtract the difference of the squares: (n + 1)^2 - n^2 n^2 + 2n + 1 - n^2 n^2 terms cancel, we get: 2n + 1 2 is even. For n, if we use an even: we have even * even = Even Add 1 we have Odd 2 is even. For n, if we use an odd: we have even * odd = Even Add 1 we have Odd Since both cases are odd, we've proven our statement. [MEDIA=youtube]RAi0HbH5bqc[/MEDIA]

Let us take an integer x which is both even [I]and[/I] odd. [LIST] [*]As an even integer, we write x in the form 2m for some integer m [*]As an odd integer, we write x in the form 2n + 1 for some integer n [/LIST] Since both the even and odd integers are the same number, we set them equal to each other 2m = 2n + 1 Subtract 2n from each side: 2m - 2n = 1 Factor out a 2 on the left side: 2(m - n) = 1 By definition of divisibility, this means that 2 divides 1. But we know that the only two numbers which divide 1 are 1 and -1. Therefore, our original assumption that x was both even and odd must be false. [MEDIA=youtube]SMM9ubEVcLE[/MEDIA]

q increased by the difference between 18 times q and 5 Take this algebraic expression in parts. 18 times q: 18q The difference between 18 times q and 5 means we subtract 5 from 18q: 18q - 5 q increased by the difference between 18 times q and 5 means we add 18q - 5 to q: q + (18q - 5) [B]q + 18q - 5[/B] IF we want to simplify, we group like terms: [B]19q - 5[/B]

Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR? From segment addition, we know that: PQ + QR = PR Plugging our given numbers in, we get: 2.7 + QR = 6.1 Subtract 2.7 from each side, and we get: 2.7 - 2.7 + QR = 6.1 - 2.7 Cancelling the 2.7 on the left side, we get: QR = [B]3.4[/B]

q is equal to 207 subtracted from the quantity 4 times q 4 time q 4q 207 subtracted from 4 times q: 4q - 207 Set this equal to q: [B]4q - 207 = q [/B]<-- This is our algebraic expression To solve for q, [URL='https://www.mathcelebrity.com/1unk.php?num=4q-207%3Dq&pl=Solve']type this equation into the search engine[/URL]. We get: [B]q = 69[/B]

q to the 10th power subtracted from 100 q to the 10th power: q^10 We subtract this from 100: [B]100 - q^10[/B]

q=c+d/5 for d Subtract c from each side to solve this literal equation: q - c = c - c + d/5 Cancel the c's on the right side, we get d/5 = q - c Multiply each side by 5: 5d/5 = 5(q - c) Cancel the 5's on the left side, we get: [B]d = 5(q - c)[/B]

q=rs/2-p;p Add p to each side: q + p = rs/2 Subtract q from each side: [B]p = rs/2 - q[/B]

r decreased by the quotient of r and 3 The quotient of r and 3 is: r/3 The phrase [I]decreased by[/I] means we subtract r/3 from r [B]r - r/3[/B]

Rachel buys some scarves that cost $10 each and 2 purses that cost $16 each. The cost of Rachel's total purchase is $62. What equation can be used to find n, the number of scarves that Rebecca buys Scarves Cost + Purses Cost = Total Cost [U]Calculate Scarves Cost[/U] Scarves cost = Cost per scarf * number of scarves Scarves cost = 10n [U]Calculate Purses Cost[/U] Purses cost = Cost per purse * number of purses Purses cost = 16 * 2 Purses cost = 32 Total Cost = 62. Plug in our numbers and values to the Total Cost equation : 10n + 32 = 62 Solve for [I]n[/I] in the equation 10n + 32 = 62 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 32 and 62. To do that, we subtract 32 from both sides 10n + 32 - 32 = 62 - 32 [SIZE=5][B]Step 2: Cancel 32 on the left side:[/B][/SIZE] 10n = 30 [SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = 30/10 n = [B]3[/B]

Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will they have the same amount? Let Rachel's account value R(w) where w is the number of weeks be: R(w) = 200 - 25w <-- We subtract -25w because she spends it every week, decreasing her balance. Let Roy's account value R(w) where w is the number of weeks be: R(w) = 15w Set them equal to each other: 200 - 25w = 15w To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=200-25w%3D15w&pl=Solve']we type it into our search engine[/URL] and get: [B]w = 5[/B]

raise 3 to the 4th power, subtract w from the result, then divide v by what you have Raise 3 to the 4th power: 3^4 Simplified, this is 81 Subtract w from the result. We subtract w from 81: 81 - w Then divide v by what you have. We divide v by (81 -w) [B]v/(81 - w)[/B]

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c. This is an algebraic expression, let's take in parts (or chunks). Raise 9 to the 3rd power. This means we take 9, and raise it to an exponent of 3 9^3 Subtract d from the result, means we subtract d from 9^3 9^3 - d Now we divide 9^3 - d by c [B](9^3 - d) / c[/B]

raise c to the 2nd power, add the result to 8, then subtract what you have from d Raise c to the 2nd power: c^2 Add the result to 8: c^2 + 8 Subtract what you have from d: d - (c^2 + 8)

raise z to the 2nd power, multiply 8 by the result then subtract what you have from 4 Take this algebraic expression in pieces: [LIST] [*]Raise z to the 2nd power: z^2 [*]Multiply by 8: 8z^2 [*]Subtract what you have from 4: [/LIST] [B]4 - 8z^2[/B]

Free Rational Number Subtraction Calculator - Subtracting 2 numbers, this shows an equivalent operations is adding the additive inverse. p - q = p + (-q)

Rearrange the following equation to make x the subject, and select the correct rearrangement from the list below 3x + 2y 1 -------- = --- 4x + y 3 [LIST] [*]x = 7y/13 [*]x = 7y/5 [*]x = -7y [*]x = -3y [*]x = 3y/5 [*]x = -5y/13 [*]x = -y [/LIST] Cross multiply: 3(3x - 2y) = 4x + y Multiply the left side through 9x - 6y = 4x + y Subtract 4x from each side and add 6y to each side 5x = 7y Divide each side by 5 to isolate x, the subject of an equation is the variable to the left [B]x = 7y/5[/B]

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random. a. What is the probability that you choose a red or even numbered ball? b. What is the probability you choose a green ball or a ball numbered less than 5? a. The phrase [I]or[/I] in probability means add. But we need to subtract even reds so we don't double count: We have 18 total balls, so this is our denonminator for our fractions. Red and Even balls are {2, 4, 6, 8, 10, 12} Our probability is: P(Red or Even) = P(Red) + P(Even) - P(Red and Even) P(Red or Even) = 13/18 + 9/18 - 6/18 P(Red or Even) = 16/18 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have: P(Red or Even) = [B]16/18[/B] [B][/B] b. The phrase [I]or[/I] in probability means add. But we need to subtract greens less than 5 so we don't double count: We have 18 total balls, so this is our denonminator for our fractions. Green and less than 5 does not exist, so we have no intersection Our probability is: P(Green or Less Than 5) = P(Green) + P(Less Than 5) - P(Green And Less Than 5) P(Green or Less Than 5) = 5/18 + 4/18 - 0 P(Green or Less Than 5) = 9/18 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have: P(Red or Even) = [B]1/2[/B]

Free Regrouping Calculator - Subtracts two numbers using regrouping

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate if 0.06 m per day. Which function can be used to find the thickness of the ice shelf in meters x days since the discovery? We want to build an function I(x) where x is the number of days since the ice shelf discovery. We start with 450 meters, and each day (x), the ice shelf loses 0.06m, which means we subtract this from 450. [B]I(x) = 450 - 0.06x[/B]

Let a be Rick's age We have a + 24 = 69 Subtract 24 from each side [B]a = 45[/B]

rs+h^2=1 for h Subtract rs from each side to isolate h: rs - rs + h^2 = 1 - rs Cancel the rs on the left side: h^2 = 1 - rs Take the square root of each side: sqrt(h^2) = sqrt(1 - rs) [B]h = +- sqrt(1 -rs)[/B]

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if he is the younger man. Let Sam's age be s. Let' Jeremy's age be j. We're given: [LIST=1] [*]s = j + 2 <-- consecutive odd integers [*]sj = 783 [/LIST] Substitute (1) into (2): (j + 2)j = 783 j^2 + 2j = 783 Subtract 783 from each side: j^2 + 2j - 783 = 0 <-- This is the equation to find Jeremy's age. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=j%5E2%2B2j-783%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this quadratic equation into the search engine[/URL] and get: j = 27, j = -29. Since ages cannot be negative, we have: [B]j = 27[/B]

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John Let John's age be j. We're given the following equation: 3j - 20 = 52 ([I]Less than[/I] means we subtract) To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get: j = [B]24[/B]

Sara opened an account with $800 and withdrew $20 per week. Jordan opened an account with $500 and deposited $30 per week. In how many weeks will their account be equal? Each week, Sara's account value is: 800 - 20w <-- Subtract because Sara withdraws money each week Each week, Jordan's account value is: 500 + 30w <-- Add because Jordan deposits money each week Set them equal to each other: 800 - 20w = 500 + 30w Using our [URL='http://www.mathcelebrity.com/1unk.php?num=800-20w%3D500%2B30w&pl=Solve']equation solver[/URL], we get w = 6. Check our work: 800 - 20(6) 800 - 120 680 500 + 30(6) 500 + 180 680

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money from her account and still have money left? Let w be the number of weeks. We have the following equation for the Balance after w weeks: B(w) = 250 - 25w [I]we subtract for withdrawals[/I] The ability to withdrawal money means have a positive or zero balance after withdrawal. So we set up the inequality below: 250 - 25w >= 0 To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=250-25w%3E%3D0&pl=Solve']type it in our search engine[/URL] and we get: w <= [B]10 So Sarah can withdrawal for up to 10 weeks[/B]

Seven less than 1/4 of a number is 9. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 1/4 of a number means we multiply x by 1/4: x/4 Seven less than this means we subtract 7 from x/4: x/4 - 7 The word [I]is[/I] means an equation, so we set x/4 - 7 equal to 9: [B]x/4 - 7 = 9[/B]

Seven subtracted from the product of 3 and a number is greater than or equal to -26 [LIST=1] [*]A number means an arbitrary variable, let's call it x. [*]The product of 3 and a number is written as 3x [*]Seven subtracted from 3x is written as 3x - 7 [*]Finally, that entire expression is greater than or equal to -26: [B]3x - 7 >= - 26[/B] [/LIST]

Shanti had 275 red beads and 3 tines as many blue beads as red beads. She used a total of 156 beads to make a bracelet how many beads did she have left? Calculate Blue Beads: Blue Beads =3 * Red Beads Blue Beads = 3(275) Blue Beads = 825 Subtract off the beads Shanti used for the bracelet: 825 - 156 = [B]669[/B]

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith? Assumptions: [LIST] [*]Let b be the number of hours Giselle worked as a blacksmith [*]Let c be the number of hours Giselle worked as a carpenter [/LIST] Givens: [LIST=1] [*]b + c = 30 [*]25b + 20c = 690 [/LIST] Rearrange equation (1) to solve for b by subtracting c from each side: [LIST=1] [*]b = 30 - c [*]25b + 20c = 690 [/LIST] Substitute equation (1) into equation (2) for b 25(30 - c) + 20c = 690 Multiply through: 750 - 25c + 20c = 690 To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=750-25c%2B20c%3D690&pl=Solve']type this equation into our search engine[/URL] and we get: c = [B]12 [/B] Now, we plug in c = 12 into modified equation (1) to solve for b: b = 30 - 12 b = [B]18[/B]

Free Signed Integer Operations Calculator - This performs a string of signed integer operations, either all addition and subtraction, or all multiplication and division.

We know from the pythagorean theorem: [SIZE=5][B]sin^2(x) + cos^2(x) = 1[/B] [B]Subtract sin^2(x) from each side and we get:[/B] [B][B]cos^2(x) = 1 - [B]sin^2(x)[/B][/B][/B] [B][B][B]We can rewrite our original expression as:[/B][/B][/B] [B][B][B]sin^2(x)/cos^2(x)[/B][/B][/B] [/SIZE] [B][B][B][SIZE=5]But this expression [/SIZE][SIZE=4]equals[/SIZE][SIZE=5] tan^2(x)[/SIZE][/B][/B][/B] [MEDIA=youtube]zqYg0VRq5Ak[/MEDIA]

Six Less than the total of three times a number and negative eight. Let's take this in pieces: Three times a number = 3x The total of this and negative eight means we subtract eight 3x - 8 Six Less than this total means we subtract 6 3x - 8 - 6 Simplify by combining like terms: [B]3x - 14[/B]

First, the phrase [I]a number[/I] means we choose an arbitrary variable, let's call it x. Twice a number means we multiply it by 2. 2x Six less than that means we subtract 6 2x - 6 Now, the last piece, we set up an inequality. At least -1 means greater than or equal to 1. At most 1 means less than or equal to 1. Notice, for both points, we include the number. -1 <= 2x - 6 <= 1

less means subtract: [B]6 - 2[/B] <-- This is our algebraic expression If we need to evaluate we have: 6 - 2 = [B]4[/B]

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. 5 times a number 5x Sixteen subtracted from five times a number 5x - 16 the number plus 4: x + 4 Equals means we set 5x - 16 equals to x + 4 for our algebraic expression: [B]5x - 16 = x + 4[/B] [B][/B] If you have to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-16%3Dx%2B4&pl=Solve']type this expression into our math solver[/URL] and we get: x = [B]5[/B]

Solve 11 - 1/2y = 3 + 6x for y Subtract 11 from each side so we can isolate the y term: 11 -11 - 1/2y = 3 + 6x - 11 Cancelling the 11's on the left side, we get: -1/2y = 6x - 8 <-- Since 3 - 11 = -8 Multiply both sides of the equation by -2 to remove the -1/2 on the left side: -2(-1/2)y = -2(6x - 8) Simplifying, we get: y = [B]-12x + 16 [MEDIA=youtube]38uwIaj88Lw[/MEDIA][/B]

Solve a= (a + b + c + d)/4 for c Cross multiply: 4a = a + b + c + d Subtract a + b+ d from each side to isolate c: 4a - a - b - d = a + b + c + d - a - b - d Canceling the a, b, and d from the right side, we get: c = [B]3a - b - d [/B]

Solve for h. rs + h^2 = l [U]Subtract rs from each side to isolate h:[/U] rs - rs + h^2 = l - rs [U]Cancel the rs terms on the left side, and we get:[/U] h^2 = l - rs [U]Take the square root of each side:[/U] h = [B]sqrt(l - rs)[/B]

Expand the right side: 1/3x + 1/2 = 6/4x - 10 Simplify as 6/4 is 3/2 x/3 + 1/2 = 3x/2 - 10 Common denominator of 2 and 3 is 6. So we have: 2x/6 + 1/2 = 9x/6 -10 Subtract 2x/6 from each side 7x/6 - 10 = 1/2 Add 10 to each side. 10 is 20/2 7x/6 = 21/2 Using our [URL='http://www.mathcelebrity.com/prop.php?num1=7x&num2=21&den1=6&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: [B]x = 9[/B]

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second. i. After how many seconds will Sophie catch Claire? ii. If the race is 500 feet, who wins? i. Sophie's distance formula is given as D = 5s Claire's distance formula is given as D = 3s + 100 Set them equal to each other 5s = 3s + 100 Subtract 3s from both sides: 2s = 100 Divide each side by 2 [B]s = 50[/B] ii. [B]Sophie since after 50 seconds, she takes the lead and never gives it back.[/B]

Squaring a number equals 5 times that number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Squaring this number: x^2 5 times this number means we multiply by 5: 5x The phrase [I]equals[/I] means we set both expressions equal to each other: [B]x^2 = 5x [/B] <-- This is our algebraic expression If you want to solve for x, then we subtract 5x from each side: x^2 - 5x = 5x - 5x Cancel the 5x on the right side, leaving us with 0: x^2 - 5x = 0 Factor out x: x(x - 5) So we get x = 0 or [B]x = 5[/B]

Stacy sells art prints for $12 each. Her expenses are $2.50 per print, plus $38 for equipment. How many prints must she sell for her revenue to equal her expenses? Let the art prints be p Cost function is 38 + 2p Revenue function is 12p Set cost equal to revenue 12p = 38 + 2p Subtract 2p from each side 10p = 38 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=10p%3D38&pl=Solve']equation calculator[/URL] gives us [B]p = 3.8[/B]

Stanley bought a ruler and a yardstick for $1.25. If the yardstick cost 45 cents more than the ruler, what was the cost of the yardstick? Let r be the cost of the ruler Let y be the cost of the yardstick We're given 2 equations: [LIST=1] [*]r + y = 1.25 [*]y = r + 0.45 [/LIST] Substitute equation (2) into equation (1) for y r + r + 0.45 = 1.25 Solve for [I]r[/I] in the equation r + r + 0.45 = 1.25 [SIZE=5][B]Step 1: Group the r terms on the left hand side:[/B][/SIZE] (1 + 1)r = 2r [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2r + 0.45 = + 1.25 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 0.45 and 1.25. To do that, we subtract 0.45 from both sides 2r + 0.45 - 0.45 = 1.25 - 0.45 [SIZE=5][B]Step 4: Cancel 0.45 on the left side:[/B][/SIZE] 2r = 0.8 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2r/2 = 0.8/2 r = 0.4 Substitute r = 0.4 into equation (2) above: y = r + 0.45 y = 0.4 + 0.45 r = [B]0.85 [URL='https://www.mathcelebrity.com/1unk.php?num=r%2Br%2B0.45%3D1.25&pl=Solve']Source[/URL][/B]

Start with t , add 6, divide by 2, then subtract 5. Start with t: t Add 6: t + 6 Divide by 2: (t + 6)/2 [I]Add parentheses because we're dividing the [U]quantity[/U] by 2 [/I] Then subtract 5: [B](t + 6)/2 - 5[/B]

Start with x , subtract 6, then times by 3. We start with x: x Subtract 6: x - 6 The phrase [I]times by[/I] means we multiply (x - 6) by 3 [B]3(x - 6) [/B] <-- This is our algebraic expression If the problem asks you to multiply through, then you'd have: 3x - 18

Stella buys one carton of juice. The carton holds 130 fl oz. She fills 5 glasses with juice from the carton. Each glass holds 8 fl oz. How much fl oz is left in the carton? First, we find out how much juice was poured into glasses from the carton: Poured Juice Weight = Glasses of Juice * Ounces per glass Poured JuiceWeight = 5 * 8 Poured JuiceWeight = 40 Next, we subtract the poured out juice weight from the full carton weight to find out the leftover amount: Leftover Juice = Carton Weight when full - Poured Juice Weight Leftover Juice = 130 - 40 Leftover Juice = [B]90 oz[/B]

Steve had $200 in his bank account. He made a deposit of $75 and then made a withdrawal of $90. How much money does Steve have in his account now? We add deposits 200 + 75 = 275 We subtract withdrawals 275 - 90 = [B]185[/B]

Storm Center 7 was tracking a cold front approaching Cedarburg. Before it rolled in, the temperature was – 7°F. Then, the temperature decreased by 9°F. What was the temperature after the cold front rolled in? Using signed integers, we start with 7 below or -7 -7 The temperature decreased by 9 which means we subtract: -7 - 9 or -7 + (-9) [B]-16°F or 16 below 0 [MEDIA=youtube]oJjEhkdnTxA[/MEDIA][/B]

Sum of w and v: w + v Square that sum (w + v)^2 Subtract 12 from the squared sum (w + v)^2 - 12

Subtract 4 from the sum of 2x and 5y. The sum of 2x and 5y means we add both terms: 2x + 5y Subtract 4 from this sum to get our algebraic expression: [B](2x + 5y) - 4[/B]

subtract 5 from the sum of 3x and 8y Take this algebraic expression in parts: [U]The sum of 3x and 8y means we add 8y to 3x:[/U] 3x + 8y [U]Subtract 5 from this sum above:[/U] [B]3x + 8y - 5[/B]

Subtract 6 from 7 times s 7 times s 7s Subtract 6 from that [B]7s - 6[/B]

Subtract 7 from p, then multiply 5 by the result. Subtract 7 from p p - 7 Multiply 5 by the result: [B]5(p - 7)[/B]

Subtract b from the sum of a and 10 The sum of a and 10 a + 10 Subtract b from this [B]a + 10 - b[/B]

subtract half of a number from 10 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x half of a number means we divide x by 2: x/2 subtract half of a number from 10 [B]10 - x/2[/B]

subtract q from r, then subtract 6 from the result Subtract q from r r - q Then subtract 6 from the results [B](r - q) - 6[/B]

subtract s from q, subtract the result from r, then double what you have Subtract s from q: q - s Subtract the result from r: r - (q - s) Then double what you have: [B]2(r - (q - s))[/B]

subtract the difference of t and s from 8 The difference of t and s: t - s Subtract this from 8: 8 - (t - s)

subtract the product of 5 and x from 7 The product of 5 and x means we multiply 5 by x: 5x We subtract this product, 5x, from 7 [B]7 - 5x[/B]

Subtract the quotient of m and 7 from 4 The quotient of m and 7 means we add divide m by 7 m/7 Subtract this quotient from 4 [B]4 - m/7[/B]

subtract w from u, triple the result, then multiply v by what you have Take this algebraic expression in 3 parts: [U]1) subtract w from u:[/U] u - w [U]2) Triple the result means we multiply u - w by 3:[/U] 3(u - w) [U]3) Multiply v by what you have. [I]What you have[/I] means the result from step 2:[/U] [B]3v(u - w)[/B]

subtract w from v, add the result to u, then triple what you have Take this algebraic expression in parts: [LIST=1] [*]Subtract w from v: v - w [*]Add the result to u (the result is #1): u + v - w [*]Triple what you have. This means multiply the result in #2 by 3: [/LIST] [B]3(u + v - w)[/B]

Subtracting 9s shortcut Add the digits of the larger number [LIST] [*]10 - 9 = 1 + 0 = 1 [*]11 - 9 = 1 + 1 = 2 [*]12 - 9 = 1 + 2 = 3 [*]13 - 9 = 1 + 3 = 4 [*]14 - 9 = 1 + 4= 5 [*]15 - 9=. 1 + 5 = 6 [*]16 - 9 = 1 + 6= 7 [*]17 - 9= 1 + 7 = 8 [*]18 - 9 = 1 + 8 = 9 [*]19 - 9 = 1 + 9 = 10 [/LIST] [MEDIA=youtube]YOHcJ6UG1D8[/MEDIA]

Free Subtraction Equality Property Calculator - Demonstrates the Subtraction Equality Property Numerical Properties

Free Subtraction Property Of Inequality Calculator - Demonstrates the Subtraction Property Of Inequality Numerical Properties

sum of 3 consecutive odd integers equals 1 hundred 17 The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers? 1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4 2) We increment by 2 for each number since we have [I]odd numbers[/I]. 3) We set this sum of consecutive [I]odd numbers[/I] equal to 117 n + (n + 2) + (n + 4) = 117 [SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE] (n + n + n) + 2 + 4 = 117 3n + 6 = 117 [SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE] 3n + 6 - 6 = 117 - 6 [SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE] 3n + [S]6[/S] - [S]6[/S] = 117 - 6 3n = 111 [SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE] 3n/3 = 111/3 [SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE] [S]3[/S]n/[S]3 [/S]= 111/3 n = 37 Call this n1, so we find our other 2 numbers n2 = n1 + 2 n2 = 37 + 2 n2 = 39 n3 = n2 + 2 n3 = 39 + 2 n3 = 41 [SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE] ([B]37, 39, 41[/B]) 37 ← 1st number, or the Smallest, Minimum, Least Value 39 ← 2nd number 41 ← 3rd or the Largest, Maximum, Highest Value

Sum of a number and 7 is subtracted from 15 the result is 6. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We take this expression in pieces. Sum of a number and 7 x + 7 Subtracted from 15 15 - (x + 7) The result is means an equation, so we set this expression above equal to 6 [B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B] If the problem asks you to solve for x, we Group like terms 15 - x - 7 = 6 8 - x = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=8-x%3D6&pl=Solve']Type 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]

Sum of a number and it's reciprocal is 6. What is the number? Let the number be n. The reciprocal is 1/n. The word [I]is[/I] means an equation, so we set n + 1/n equal to 6 n + 1/n = 6 Multiply each side by n to remove the fraction: n^2 + 1 = 6n Subtract 6n from each side: [B]n^2 - 6n + 1 = 0 [/B]<-- This is our algebraic expression If the problem asks you to solve for n, then you [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-6n%2B1%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this quadratic equation into our search engine[/URL].

Super Snack, a convenience store, charges $4.35 for a large chicken sandwich and two large colas. For a large chicken sandwich and a large cola, they charge $4.00. How much are the Super Snack large chicken sandwiches? The difference between the orders is $0.35 and 1 large cola. Therefore, 1 large cola = $0.35. And if we use the first order of one large chicken sandwich and one large cola, we get: Large Chicken Sandwich + 0.35 = 4.35 Subtract 0.35 from each side, and we get: Large Chicken Sandwich = $[B]4.00[/B]

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin does she have? Set up two equations where d is the number of dimes and q is the number of quarters: (1) d + q = 10 (2) 0.1d + 0.25q = 1.45 Rearrange (1) into (3) to solve for d (3) d = 10 - q Now plug (3) into (2) 0.1(10 - q) + 0.25q = 1.45 Multiply through: 1 - 0.1q + 0.25q = 1.45 Combine q terms 0.15q + 1 = 1.45 Subtract 1 from each side 0.15q = 0.45 Divide each side by 0.15 [B]q = 3[/B] Plug our q = 3 value into (3) d = 10 - 3 [B]d = 7[/B]

T = mg - mf for f Subtract mg from each side: T - mg = mg - mg - mf Cancel the mg on the right side and we get: T - mg = -mf Multiply each side by -1: -(T - mg) = -(-mf) mg - T = mf Now Divide each side by m to isolate f: (mg - T)/m = mf/m Cancel the m on the right side and we get: f = [B](mg - T)/m[/B]

The cube of e is e^3. Take away 1 means subtract 1 e^3 - 1

take away the product of 12 and p from 25 The product of 12 and p means we multiply 12 by p: 12p Take away this product means we subtract 12p from 25: [B]25 - 12p[/B]

Ten subtracted from the product of 9 and a number is less than −24. A number means an arbitrary variable, let's call it x x The product of 9 and a number: 9x Ten subtracted from that 9x - 10 Finally, is less than means we set our entire expression less than -24 [B]9x - 10 < -24[/B]

Terry recorded the temperature every hour from 8 AM to 1 PM. The temperature at 8 AM was 19˚. The temperature dropped 4˚ every hour. What was the temperature at 1 PM? Group of answer choices 1 degree Set up our temperature function T(h) where h is the number of hours since 8 AM: T(h) = 19 - 4h <-- We subtract 4h since each hour, the temperature drops 4 degrees The questions asks for the temperature at 1PM. We need to figure out how many hours pass since 8 AM: 8 AM to 12 PM is 4 hours 12 PM to 1 PM is 1 hour Total time is 5 hours So we want T(5): T(5) = 19 - 4(5) T(5) = 19 - 20 T(5) = [B]-1˚[/B]

the absolute value of the difference 6 and k The difference of 6 and k means we subtract k from 6: 6 - k Take the absolute value: [B]|6 - k|[/B]

The age of a woman 15 years ago Let the woman's current age be a. 15 years ago means we subtract 15 from a: [B]a - 15[/B]

The age of denver 3 years ago if he is x years old now 3 years ago means we subtract: [B]x - 3[/B]

The age of woman 15 years ago Let a be the woman's age today. 15 years ago means we subtract 15 from a: [B]a - 15[/B]

The book Shelly has 235 pages. she has read 110 pages. If she reads 25 pages from now on, how many more days will it take her to complete the book? Subtract the pages read to get the unread pages: 235 - 110 = 125 unread pages Now figure out how many days, reading 25 pages per day, to read 125 pages 125/25 = [B]5 days[/B]

The club uses the function S(t) = -4,500t + 54,000 to determine the salvage S(t) of a fertilizer blender t years after its purchase. How long will it take the blender to depreciate completely? Complete depreciation means the salvage value is 0. So S(t) = 0. We need to find t to make S(t) = 0 -4,500t + 54,000 = 0 Subtract 54,000 from each side -4,500t = -54,000 Divide each side by -4,500 [B]t = 12[/B]

The cost of purchasing a hockey stick and puck if the stick costs 6 less than twice the cost of the puck. Let the hockey stick cost h, and puck cost p. Twice the cost of the puck means we multiply p by 2: 2p 6 less than this means we subtract 6: h = 2p - 6 [B][/B] The total cost of the hockey stick and puck is: p + 2p - 6 [B]3p - 6[/B]

The cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. How long can a person have the rototiller if the cost must be less than $95? Setup the inequality: $19.50 + $7.95x < $95 Subtract 19.50 from both sides: 7.95x < 75.50 Divide each side of the inequality by 7.95 to isolate x x < 9.5 The next lowest integer is 9. So we take 9 + the first hour of renting to get [B]10 total hours[/B]. Check our work: $7.95 * 9.5 + $19.50 $71.55 + $19.50 = $91.05

the cube of c decreased by a^2 The cube of means we raise the variable c to the power of 3: c^3 The phrase [I]decreased by[/I] means we subtract: [B]c^3 - a^2[/B]

the cube of the difference of 5 times x and 4 Take this algebraic expression in pieces: 5 times x: 5x The difference of 5x and 4 means we subtract 4 from 5x: 5x - 4 We want to cube this difference, which means we raise the difference to the power of 3. [B](5x - 4)^3[/B]

Draw this rectangle and you'll see we have a pythagorean theorem equation. a^2 + b^2= c^2 b = 8 and c= 10 a^2 + 8^2 = 10^2 a^2 + 64 = 100 Subtract 64 from each side: a^2 = 36 a= 6 Therefore, perimeter P is: P = 2l + 2w P = 2(6) + 2(8) P = 12 + 16 P = [B]28[/B] [MEDIA=youtube]8lcpRet3r18[/MEDIA]

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers? Let the smaller number be x. Let the larger number be y. We're given: [LIST=1] [*]y - x = 108 [*]6x = y + 2 [/LIST] Rearrange (1) by adding x to each side: [LIST=1] [*]y = x + 108 [/LIST] Substitute this into (2): 6x = x + 108 + 2 Combine like terms 6x = x +110 Subtract x from each side: 5x = 110 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D110&pl=Solve']Plugging this equation into our search engine[/URL], we get: x = [B]22[/B]

[U]3 times x:[/U] 3x [U]The difference between 3x and 4 means we subtract:[/U] 3x - 4

the difference between 7 times a number and 9 less than a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 7 times a number means we multiply x by 7 7x 9 less than a number means we subtract 9 from x x - 9 The difference between the two expressions means we subtract (x - 9) from 7x 7x - (x - 9) Simplifying this, we have: 7x - x + 9 Grouping like terms, we get: [B]6x + 9[/B]

The difference between a and b is 10. The problem asks for an algebraic expression. Let's take each piece one by one: [I]Difference between[/I] means we subtract: a - b The phrase [I]is [/I]means an equation, so we set a - b equal to 10 [B]a - b = 10[/B]

The difference between A and B is no less than 30 The difference between means we subtract. No less than means greater than or equal to, so we have the following inequality; [B]A - B >= 30[/B]

The difference between sixty-four and y The difference between means we subtract y from 64: [B]64 - y[/B]

The difference between the opposite of a number and 6. The phrase [I]a number means[/I] an arbitrary variable, let's call it x. x The opposite of a number means we multiply by x by -1 -x The phrase [I]the difference between[/I] means we subtract 6 from -x: [B]-x - 6[/B]

The difference between the quotient of x and y, and twice z The quotient of x and y means we divide x by y: x/y Twice z means we multiply z by 2: 2z The difference between the quotient of x and y, and twice z means we subtract 2z from x/y [B]x/y - 2z[/B]

The difference between the square of b and the total of b and 9 The square of b means we raise b to the power of 2: b^2 The total of b and 9 means we add 9 to b: b + 9 The difference means we subtract: [B]b^2 - (b + 9)[/B]

the difference between triple a number and double a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Triple a number means we multiply x by 3: 3x Double a number means we multiply x by 2: 2x The difference means we subtract 2x from 3x: 3x - 2x Simplifying like terms, we have: (3 - 2)x = [B]x[/B]

The difference in Julies height and 9 is 48 letting j be Julie's height Step 1: If Julie's height is represented with the variable j, then we subtract 9 from j since the phrase [I]difference[/I] means we subtract: j - 9 Step 2: The word [I]is[/I] means an equation, so we set j - 9 equal to 48 for our final algebraic expression: [B]j - 9 = 48[/B]

The difference of 100 and x means we subtract x from 100: 100 - x Is means equal to, so we set our expression above equal to 57 [B]100 - x = 57 [/B] If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=100-x%3D57&pl=Solve']equation calculator[/URL]

The difference of 25 and a number added to triple another number The phrase [I]a number [/I]means an arbitrary variable, let's call it x: x The difference of 25 and a number means we subtract x from 25: 25 - x The phrase [I]another number[/I] means a different arbitrary variable, let's call it y: y Triple another number means we multiply y by 3: 3y The phrase [I]added to[/I] means we add 25 - x to 3y [B]25 - x + 3y[/B]

the difference of 4 and the quotient of 18 and a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The quotient of 18 and a number means we divide 18 by the variable x. 18/x The difference of 4 and the quotient above means we subtract 18/x from 4: [B]4 - 18/x[/B]

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number? We have two expressions: [U]Expression 1: [I]The difference of a number and 6[/I][/U] The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The difference of a number and 6 means we subtract 6 from x: x - 6 [U]Expression 2: [I]5 times the sum of the number and 2[/I][/U] The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The sum of a number and 2 means we add 2 to x: x + 2 5 times the sum means we multiply x + 2 by 5 5(x + 2) [U]For the last step, we evaluate the expression [I]is the same as[/I][/U] This means equal to, so we set x - 6 equal to 5(x + 2) [B]x - 6 = 5(x + 2)[/B]

The difference of five and five y 5 - 5y eight and two y 8 + 2y The phrase [I]is the same as[/I] means equal to. Set 5 - 5y equal to 8 + 2y for our final algebraic expression [B]5 - 5y = 8 + 2y[/B] [B][/B] If the problem asks you to solve for y: Add 5y to each side: 5 = 8 + 7y Subtract 8 from each side: 7y = -3 Divide each side by 7: [B]y= -3/7[/B]

The difference of twice a number and 6 is at most 28 This is an algebraic expression. Let's take it in parts: [LIST=1] [*]The phrase [I]a number[/I], means an arbitrary variable, let's call it x [*]Twice this number means we multiply x by 2: 2x [*][I]The difference of[/I] means subtract, so we subtract 6 to 2x: 2x - 6 [*][I]Is at most [/I]means less than or equal to, so we create an inequality where 2x - 6 is less than or equal to 28, using the <= sign [/LIST] [B]2x - 6 <= 28 [/B] If you wish to solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-6%3C%3D28&pl=Solve']click this link[/URL].

the difference of twice a number and 8 is at most -30. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Twice this number means we multiply by 2, so we have 2x. We take the difference of 2x and 8, meaning we subtract 8: 2x - 8 Finally, the phrase [I]at most[/I] means an inequality, also known as less than or equal to: [B]2x - 8 <= 30 <-- This is our algebraic expression [/B] To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-8%3C%3D30&pl=Solve']type it into the search engine[/URL] and get x <= 19.

the difference of x and 5 is 2 times of x The difference of x and 5 means we subtract 5 from x x - 5 The word [I]is[/I] means an equation, so we set x - 5 equal to 2 times x [B]x - 5 = 2x[/B]

The difference of x and x squared We subtract x^2 from x: [B]x - x^2[/B]

The difference when (10x - 6y) is subtracted from (7x - 4y) In simplest form (7x - 4y) - (10x - 6y) 7x - 4y - 10x - -6y 7x - 4y - 10x + 6y (7 - 10)x + (-4 + 6)y [B]-3x + 2y[/B]

The enrollment at High School R has been increasing by 20 students per year. High School R currently has 200 students. High School T has 400 students and is decreasing 30 students per year. When will the two school have the same enrollment of students? Set up the Enrollment function E(y) where y is the number of years. [U]High School R:[/U] [I]Increasing[/I] means we add E(y) = 200 + 20y [U]High School T:[/U] [I]Decreasing[/I] means we subtract E(y) = 400 - 30y When the two schools have the same enrollment, we set the E(y) functions equal to each other 200 + 20y = 400 - 30y To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=200%2B20y%3D400-30y&pl=Solve']type it in our search engine[/URL] and we get: y = [B]4[/B]

The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and the ticket price are in dollars. What is the maximum profit, and how much should the tickets cost? Take the [URL='http://www.mathcelebrity.com/dfii.php?term1=-30x%5E2+%2B+360x+%2B+785&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']derivative of the profit function[/URL]: P'(x) = -60x + 360 We find the maximum when we set the profit derivative equal to 0 -60x + 360 = 0 Subtract 360 from both sides: -60x = -360 Divide each side by -60 [B]x = 6 <-- This is the ticket price to maximize profit[/B] Substitute x = 6 into the profit equation: P(6) = -30(6)^2 + 360(6) + 785 P(6) = -1080 + 2160 + 785 [B]P(6) = 1865[/B]

The negative of the sum of C and D is equal to the difference of the negative of C and D The negative of the sum of C and D means -1 times the sum of C and D -(C + D) Distribute the negative sign: -C - D the difference of the negative of C and D means we subtract D from negative C -C - D So this statement is [B]true[/B] since -C - D = -C - D

The next number in the series 38 36 30 28 22 is Notice the change of factors. Subtract 2, Subtract 6, Subtract 2, Subtract 6. So the next number should subtract 2. 22 - 2 = [B]20 [MEDIA=youtube]x7SHk_6-aok[/MEDIA][/B]

The number -2.34 can be found between which two integers We want to take the integer of -2.34 which is -2 Since -2.34 is less than 0, we subtract 1: -2 -1 = -3 Therefore, -2.34 lies between [B]-2 and -3[/B] -3 < -2.34 < -2

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000. [LIST] [*]h = b + 70 [*]A = 1/2bh = 3000 [/LIST] Substitute the height equation into the area equation 1/2b(b + 70) = 3000 Multiply each side by 2 b^2 + 70b = 6000 Subtract 6000 from each side: b^2 + 70b - 6000 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=b%5E2%2B70b-6000%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: b = 50 and b = -120 Since the base cannot be negative, we use b = 50. If b = 50, then h = 50 + 70 = 120 The perimeter is b + h + hypotenuse Using the [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=70&angle_b=&b=50&c=&pl=Calculate+Right+Triangle']right-triangle calculator[/URL], we get hypotenuse = 86.02 Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company called Rachel and offered her long distance service for 1/2 cent per minute, but will charge a $46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a better deal? Minutes Rachel talks = m Current plan cost = 0.12m New plan cost = 0.005m + 46 Set new plan equal to current plan: 0.005m + 46 = 0.12m Solve for [I]m[/I] in the equation 0.005m + 46 = 0.12m [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 0.005m and 0.12m. To do that, we subtract 0.12m from both sides 0.005m + 46 - 0.12m = 0.12m - 0.12m [SIZE=5][B]Step 2: Cancel 0.12m on the right side:[/B][/SIZE] -0.115m + 46 = 0 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 46 and 0. To do that, we subtract 46 from both sides -0.115m + 46 - 46 = 0 - 46 [SIZE=5][B]Step 4: Cancel 46 on the left side:[/B][/SIZE] -0.115m = -46 [SIZE=5][B]Step 5: Divide each side of the equation by -0.115[/B][/SIZE] -0.115m/-0.115 = -46/-0.115 m = [B]400 She must talk over 400 minutes for the new plan to be a better deal [URL='https://www.mathcelebrity.com/1unk.php?num=0.005m%2B46%3D0.12m&pl=Solve']Source[/URL][/B]

The points -5, -24 and 5,r lie on a line with slope 4. Find the missing coordinate r. Slope = (y2 - y1)/(x2 - x1) Plugging in our numbers, we get: 4 = (r - -24)/(5 - -5) 4 = (r +24)/10 Cross multiply: r + 24 = 40 Subtract 24 from each side: [B]r = 16[/B]

the product of 2 less than a number and 7 is 13 Take this algebraic expression in [U]4 parts[/U]: Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x Part 2 - 2 less than a number means we subtract 2 from x x - 2 Part 3 - The phrase [I]product[/I] means we multiply x - 2 by 7 7(x - 2) Part 4 - The phrase [I]is[/I] means an equation, so we set 7(x - 2) equal to 13 [B]7(x - 2) = 13[/B]

the product of k and 70, minus 15 Take this algebraic expression in pieces: The product of k and 70 means we multiply 70 times k 70k The word [I]minus[/I] means we subtract 15 from 70k [B]70k - 15[/B]

The product of two consecutive integers is greater than 100 Take an integer x. Next consecutive integer is x + 1 The product of those integers is: x(x + 1) This product is greater than 100 which gives us the algebraic expression of: x(x + 1) > 100 IF we want to solve for x: x^2 + x > 100 Subtract 100 from each side: x^2 + x - 100 > 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-100%3E0&pl=All&hintnum=+0']Solve this quadratic:[/URL]

The product of two positive numbers is 96. Determine the two numbers if one is 4 more than the other. Let the 2 numbers be x and y. We have: [LIST=1] [*]xy = 96 [*]x = y - 4 [/LIST] [U]Substitute (2) into (1)[/U] (y - 4)y = 96 y^2 - 4y = 96 [U]Subtract 96 from both sides:[/U] y^2 - 4y - 96 = 0 [U]Factoring using our quadratic calculator, we get:[/U] (y - 12)(y + 8) So y = 12 and y = -8. Since the problem states positive numbers, we use [B]y = 12[/B]. Substituting y = 12 into (2), we get: x = 12 - 4 [B]x = 8[/B] [B]We have (x, y) = (8, 12)[/B]

the quotient of 4 more than a number and 7 is 10 Take this algebraic expression in pieces: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 more than a number means we add 4 to x: x + 4 The quotient of 4 more than a number and 7 means we divide x + 4 by 7 (x + 4)/7 The word [I]is[/I] means an equation, so we set (x + 4)/7 equal to 10 to get our algebraic expression of: [B](x + 4)/7 = 10 [/B] If the problem asks you to solve for x, then we cross multiply: x + 4 = 10 * 7 x + 4 = 70 Subtract 4 from each side: x + 4 - 4 = 70 - 4 x = [B]66 [MEDIA=youtube]j-GZLPVKbTM[/MEDIA][/B]

The difference of x and m means we subtract: x - m Quotient means a fraction. 8 is the numerator, and x - m is the denominator: [B] 8 ------ x - m[/B]

The Square of a positive integer is equal to the sum of the integer and 12. Find the integer Let the integer be x. [LIST] [*]The sum of the integer and 12 is written as x + 12. [*]The square of a positive integer is written as x^2. [/LIST] We set these equal to each other: x^2 = x + 12 Subtract x + 12 from each side: x^2 - x - 12 = 0 We have a quadratic function. [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-x-12%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Run it through our search engine[/URL] and we get x = 3 and x = -4. The problem asks for a positive integer, so we have [B]x = 3[/B]

The square of a positive integer minus twice its consecutive integer is equal to 22. Find the integers. Let x = the original positive integer. We have: [LIST] [*]Consecutive integer is x + 1 [*]x^2 - 2(x + 1) = 22 [/LIST] Multiply through: x^2 - 2x - 2 = 22 Subtract 22 from each side: x^2 - 2x - 24 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2-2x-24%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: x = 6 and x = -4 Since the problem states [U]positive integers[/U], we use: x = 6 and x + 1 = 7 [B](6, 7)[/B]

Write this out, let the number be x. sqrt(2x) = x - 4 since 4 less means subtract Square each side: sqrt(2x)^2 = (x - 4)^2 2x = x^2 - 8x + 16 Subtract 2x from both sides x^2 - 10x + 16 = 0 Using the [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2+-+10x+%2B+16+%3D+0&pl=Solve+Quadratic+Equation&hintnum=0']quadratic calculator[/URL], we get two potential solutions x = (2, 8) Well, 2 does not work, since sqrt(2*2) = 2 which is not 4 less than 2 However, 8 does work: sqrt(2*8) = sqrt(16) = 4, which is 4 less than the number 8.

The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers? Let the first number be x. And the second number be y. We're given: [LIST=1] [*]y = x + 1 [*]x + y = 3x - 3 (less 3 means subtract 3) [/LIST] Substitute (1) into (2): x + x + 1 = 3x - 3 Combine like terms: 2x + 1 = 3x - 3 [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B1%3D3x-3&pl=Solve']Type this equation into the search engine[/URL], we get: x = 4 Substituting x = 4 into equation 1: y = 4 + 1 y = 5 So (x, y) = [B](4, 5)[/B]

The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find the numbers. Let the first number be x. The second number is y. We have: [LIST=1] [*]x + y = 18 [*]3x = 4y + 5 [/LIST] Rearrange (2), by subtracting 4y from each side: 3x - 4y = 5 So we have a system of equations: [LIST=1] [*]x + y = 18 [*]3x - 4y = 5 [/LIST] Using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+18&term2=3x+-+4y+%3D+5&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [B]x = 11 y = 7[/B]

The sum of 2 numbers is 70. The difference of these numbers is 24. Write and solve a system of equations to determine the numbers. Let the two numbers be x and y. We have the following equations: [LIST=1] [*]x + y = 70 [*]x - y = 24 [/LIST] Add (1) to (2): 2x = 94 Divide each side by 2 [B]x = 47[/B] Plug this into (1) 47 + y = 70 Subtract 47 from each side, we have: [B]y = 23[/B]

the sum of 2 times a number and -2, added to 4 times a number. The phrase, [I]a number[/I], means an arbitrary variable, let's call it x. 2 times a number 2x The sum of means add, so we add -2, which is the same as subtracting 2 2x - 2 Now, we add 4 times x 2x - 2 + 4x Combining like terms, we have: (2 + 4)x - 2 [B]6x - 2[/B]

The sum of a number and its square is 72. find the numbers? Let the number be n. We have: n^2 + n = 72 Subtract 72 from each side: n^2 + n - 72 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-72%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we have: [B]n = 8 or n = -9 [/B] Since the numbers do not state positive or negative, these are the two solutions.

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages? [U]Givens[/U] [LIST] [*]Let Mr. Adam's age be a [*]Let Mrs. Benson's age be b [*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract: [/LIST] [LIST=1] [*]a + b = 55 [*]a - b = 3 [/LIST] Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2: (a + a) + (b - b) = 55 + 3 Combining like terms and simplifying, we get: 2a = 58 To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=2a%3D58&pl=Solve']type it in our search engine[/URL] and we get: a = [B]29 [/B] If a = 29, then we plug this into equation (1) to get: 29 + b = 55 b = 55 - 29 b = [B]26 [MEDIA=youtube]WwkpNqPvHs8[/MEDIA][/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now? Let Levi's current age be l. Let Renee's current age be r. Were given two equations: [LIST=1] [*]l + r = 89 [*]l - 7 = 4(r - 7) [/LIST] Simplify equation 2 by multiplying through: [LIST=1] [*]l + r = 89 [*]l - 7 = 4r - 28 [/LIST] Rearrange equation 1 to solve for r and isolate l by subtracting l from each side: [LIST=1] [*]r = 89 - l [*]l - 7 = 4r - 28 [/LIST] Now substitute equation (1) into equation (2): l - 7 = 4(89 - l) - 28 l - 7 = 356 - 4l - 28 l - 7 = 328 - 4l To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get: l = [B]67[/B]

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number. Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given: [LIST=1] [*]x + y = 10 [*]10x+ y = 15y + 4 [/LIST] Simplifying Equation (2) by subtracting y from each side, we get: 10x = 14y + 4 Rearranging equation (1), we get: x = 10 - y Substitute this into simplified equation (2): 10(10 - y) = 14y + 4 100 - 10y = 14y + 4 [URL='https://www.mathcelebrity.com/1unk.php?num=100-10y%3D14y%2B4&pl=Solve']Typing this equation into our search engine[/URL], we get: y = 4 Plug this into rearranged equation (1), we get: x = 10 - 4 x = 6 So our number xy is [B]64[/B]. Let's check our work against equation (1): 6 + 4 ? 10 10 = 10 Let's check our work against equation (2): 10(6)+ 4 ? 15(4) + 4 60 + 4 ? 60 + 4 64 = 64

The sum of the squares of two consecutive positive integers is 61. Find these two numbers. Let the 2 consecutive integers be x and x + 1. We have: x^2 + (x + 1)^2 = 61 Simplify: x^2 + x^2 + 2x + 1 = 61 2x^2 + 2x + 1 = 61 Subtract 61 from each side: 2x^2 + 2x - 60 = 0 Divide each side by 2 x^2 + x - 30 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-30&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL], we get: x = 5 and x = -6 The question asks for [I]positive integers[/I], so we use [B]x = 5. [/B]This means the other number is [B]6[/B].

Let the 3 integers be x, y, and z. y = x + 1 z = y + 1, or x + 2. Set up our equation: x + (x + 1) + (x + 2) = 42 Group our variables and constants: (x + x + x) + (1 + 2) = 42 3x + 3 = 42 Subtract 3 from each side: 3x = 39 Divide each side of the equation by 3: [B]x = 13 So y = x + 1 = 14 z = x + 2 = 15 (x,y,z) = (13,14,15)[/B]

The sum of twice an integer and 3 times the next consecutive integer is 48 Let the first integer be n This means the next consecutive integer is n + 1 Twice an integer means we multiply n by 2: 2n 3 times the next consecutive integer means we multiply (n + 1) by 3 3(n + 1) The sum of these is: 2n + 3(n + 1) The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48: 2n + 3(n + 1) = 48 Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48 We first need to simplify the expression removing parentheses Simplify 3(n + 1): Distribute the 3 to each term in (n+1) 3 * n = (3 * 1)n = 3n 3 * 1 = (3 * 1) = 3 Our Total expanded term is 3n + 3 Our updated term to work with is 2n + 3n + 3 = 48 We first need to simplify the expression removing parentheses Our updated term to work with is 2n + 3n + 3 = 48 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 + 3)n = 5n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 5n + 3 = + 48 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 48. To do that, we subtract 3 from both sides 5n + 3 - 3 = 48 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 5n = 45 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5n/5 = 45/5 Cancel the 5's on the left side and we get: n = [B]9[/B]

The sum of two y and three 2y + 3 the difference of three y and one 3y - 1 is the same as means equal to. Set 2y + 3 equal to 3y - 1 for our final algebraic expression: [B]2y + 3 = 3y - 1[/B] [B][/B] If the problem asks you to solve for y, subtract 2y from each side: 3 = y - 1 Add 1 to each side: y = [B]4[/B]

The sum of y and z decreased by the difference of m and n. Take this algebraic expression in 3 parts: [LIST=1] [*]The sum of y and z means we add z to y: y + z [*]The difference of m and n means we subtract n from m: m - n [*]The phrase [I]decreased by[/I] means we subtract the quantity (m - n) from the sum (y + z) [/LIST] [B](y + z) - (m - n)[/B]

The temperature in Chicago was five (5) degrees Celsius in the morning and is expected to drop by as much as 12 degrees during the day. What is the lowest temperature in Chicago for the day? We start with 5 celsius A drop in temperature means we subtract 5 - 12 = [B]-7 or 7 degrees below zero[/B]

The temperature was 7℉ below zero. The temperature drops by 6℉. What is the temperature now Below zero means negative. A drop means we subtract, so we have: [LIST] [*]7 below zero = -7 [*]Drops by 6 = -6 [*]-7 - 6 = [B]-13[/B] [/LIST]

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins? Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given: [LIST=1] [*]a + h + c = 48 [*]a = 0.5h [*]a = c + 4 [/LIST] To isolate equations in terms of Suresh's age (a), let's do the following: [LIST] [*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4 [*]Rewriting (2) by multiply each side by 2, we have h = 2a [/LIST] We have a new system of equations: [LIST=1] [*]a + h + c = 48 [*]h = 2a [*]c = a - 4 [/LIST] Plug (2) and (3) into (1) a + (2a) + (a - 4) = 48 Group like terms: (1 + 2 + 1)a - 4 = 48 4a - 4 = 48 [URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]a = 13 [/B]<-- Suresh's age This means that Hakima's age, from modified equation (2) above is: h = 2(13) [B]h = 26[/B] <-- Hakima's age This means that Saad's age, from modified equation (3) above is: c = 13 - 4 [B]c = 9[/B] <-- Saad's age [B] [/B]

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take? Set up the earnings equation for the volleyball team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 4w + 81 Set up the earnings equation for the wrestling team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 2w + 85 If the raised the same amount in total, set both earnings equations equal to each other: 4w + 81 = 2w + 85 Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides 4w + 81 - 2w = 2w + 85 - 2w [SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE] 2w + 81 = 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 81 and 85. To do that, we subtract 81 from both sides 2w + 81 - 81 = 85 - 81 [SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE] 2w = 4 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 4/2 w = [B]2 <-- How many cars it will take [/B] To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2: E = 4(2) + 81 E = 8 + 81 E = [B]89 <-- Total Earnings[/B]

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How many of each animal are there? Chickens have 2 legs, pigs have 4 legs. Let c be the number of chickens and p be the number of pigs. Set up our givens: (1) c + p = 13 (2) 2c + 4p = 40 [U]Rearrange (1) to solve for c by subtracting p from both sides:[/U] (3) c = 13 - p [U]Substitute (3) into (2)[/U] 2(13 - p) + 4p = 40 26 - 2p + 4p = 40 [U]Combine p terms[/U] 2p + 26 = 40 [U]Subtract 26 from each side:[/U] 2p = 14 [U]Divide each side by 2[/U] [B]p = 7[/B] [U]Substitute p = 7 into (3)[/U] c = 13 - 7 [B]c = 6[/B] For a shortcut, you could use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+p+%3D+13&term2=2c+%2B+4p+%3D+40&pl=Cramers+Method']simultaneous equations calculator[/URL]

There are 2 consecutive integers. Twice the first increased by the second yields 16. What are the numbers? Let x be the first integer. y = x + 1 is the next integer. We have the following givens: [LIST=1] [*]2x + y = 16 [*]y = x + 1 [/LIST] Substitute (2) into (1) 2x + (x + 1) = 16 Combine x terms 3x + 1 = 16 Subtract 1 from each side 3x = 15 Divide each side by 3 [B]x = 5[/B] So the other integer is 5 + 1 = [B]6[/B]

There are 4 fewer peaches than lemons on a table. If there are x lemons, how many peaches are there? Fewer means subtract: [B]x - 4[/B]

[SIZE=6]There are 812 students in a school. There are 36 more girls than boys. How many girls are there? Let b be boys Let g be girls We're given two equations:[/SIZE] [LIST=1] [*][SIZE=6]b + g = 812[/SIZE] [*][SIZE=6]g = b + 36[/SIZE] [/LIST] [SIZE=6]Rearrange equation 2 to subtract b from each side: [/SIZE] [LIST=1] [SIZE=6] [LIST][*]b + g = 812[/LIST] [LIST][*]-b + g = 36[/LIST][/SIZE] [/LIST] [SIZE=6]Add equation (1) to equation (2): b - b + 2g = 812 + 36 The b's cancel: 2g = 848 Divide each side by 2: 2g/2 = 848/2 g = [B]424[/B] [B][/B] To find b, we put g= 424 into equation 1: b + 424 = 812 b = 812 - 424 b = [B]388[/B] [MEDIA=youtube]JO1b7qVwWoI[/MEDIA] [/SIZE]

There are 85 students in a class, 40 of them like math,31 of them like science, 12 of them like both, how many don't like either. We have the following equation: Total Students = Students who like math + students who like science - students who like both + students who don't like neither. Plug in our knowns, we get: 85 = 40 + 31 - 12 + Students who don't like neither 85 = 59 + Students who don't like neither Subtract 59 from each side, we get: Students who don't like neither = 85 - 59 Students who don't like neither = [B]26[/B]

There was 35 balloons at the beginning of a party. By the end of the party, n of them had popped. Using n, write an expression for the number of balloons that were left. We start with 35, we take away or subtract n that popped. We're left with: [B]35 - n[/B]

Set up two equations: (1) b = g + 16 (2) b + g = 150 Substitute equation (1) into (2) (g + 16) + g = 150 Combine like terms 2g + 16 = 150 Subtract 16 from each side 2g = 134 Divide each side by 2 to isolate g g = 67 Substitute this into equation (1) b = 67 + 16 [B]b = 83[/B]

There were 76 frogs in a pond. F of the frogs hopped away. How many are there in the pond now? Start with 76. F hop away meaning we subtract F. [B]76 - F[/B]

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number Let's call our number n. Double the number means we multiply n by 2: 2n Subtract 6 from the result means we subtract 6 from 2n: 2n - 6 Divide the answer by 2: (2n - 6)/2 We can simplify this as n - 3 The quotient will be 20. This means the simplified term above is set equal to 20: [B]n - 3 = 20 [/B] <-- This is our algebraic expression If you want to take it a step further, and solve for n in the algebraic expression above, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-3%3D20&pl=Solve']type this expression into our calculator[/URL], and get: n = 23

Three subtracted from triple a number A number means an arbitrary variable, let's call it x x Triple it 3x Three subtracted from this [B]3x - 3[/B]

Twice x means we multiply x by 2: 2x five less than twice x 2x - 5 Three x 3x The word [I]is[/I] means equal to. Set 2x - 5 equal to 3x for our algebraic expression: [B]2x - 5 = 3x [/B] If the problem asks you to solve for x, subtract 2x from each side [B]x = -5[/B]

Tiffany is 59 years old. The sum of the ages of Tiffany and Maria is 91. How old is Maria? Tiffany + Maria = 91 59 + Maria = 91 Subtract 59 from each side Maria = 91 - 59 [B]Maria = 32[/B]

Let h be the number of hours that pass when Charlie starts. We have the following equations: [LIST] [*]Charlie: D = 40h + 9 [*]Danny: D = 55h [/LIST] Set them equal to each other: 40h + 9 = 55h Subtract 40h from both sides: 15h = 9 h = 3/5 [B]3/5 of an hour = 3(60)/5 = 36 minutes[/B]

Thank you so much [QUOTE="math_celebrity, post: 1003, member: 1"]Let h be the number of hours that pass when Charlie starts. We have the following equations: [LIST] [*]Charlie: D = 40h + 9 [*]Danny: D = 55h [/LIST] Set them equal to each other: 40h + 9 = 55h Subtract 40h from both sides: 15h = 9 h = 3/5 [B]3/5 of an hour = 3(60)/5 = 36 minutes[/B][/QUOTE]

Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill? Let t be Tom's age., s be Sue's age, and b be Bill's age. We have the following equations: [LIST=1] [*]t = s + 2 [*]b = 2t [*]s + t + b - 2 = 20 [/LIST] Get (2) in terms of s (2) b = 2(s + 2) <-- using (1), substitute for t So we have (3) rewritten with substitution as: s + (s + 2) + 2(s + 2) - 2 = 20 s + (s + 2) + 2s + 4 - 2 = 20 Group like terms: (s + s + 2s) + (2 + 4 - 2) = 20 4s + 4 = 20 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B4%3D20&pl=Solve']equation calculator [/URL]to get s = 4 Above, we had b = 2(s + 2) Substituting s = 4, we get: 2(4 + 2) = 2(6) = [B]12 Bill is 12 years old[/B]

Translate this phrase into an algebraic expression. 57 decreased by twice Mais savings Use the variable m to represent Mais savings. Twice means multiply by 2 2m 57 decreased by means subtract 2m from 57 [B]57 - 2m[/B]

Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variable d to represent Diegos age. The difference means we subtract, so we have d as Diego's age minus 17 d - 17 The word "is" means an equation, so we set d - 17 equal to 49 [B]d - 17 = 49[/B]

The triangle sum theorem states the sum of the three angles in a triangle equals 180 degrees. So if you're given two angles and need too find the 3rd angle, add the 2 known angles up, and subtract them from 180 to get the 3rd angle measure.

triple c, multiply the result by a, then subtract b Triple c means we multiply c by 3: 3c Multiply the result by a means we multiply 3c by a 3ac Then, we subtract b from 3ac: [B]3ac - b[/B]

Free True False Equations Calculator - Determines if a set of addition and subtraction of numbers on each side of an equation are equivalent. Also known as true or false equations

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. Twice a number means we multiply x by 2: 2x Decreased by six means we subtract 6 from 2x: [B]2x - 6[/B]

twice a number subtracted from the square root of the same number The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Twice a number means we multiply x by 2: 2x Square root of the same number: sqrt(x) twice a number subtracted from the square root of the same number [B]sqrt(x) - 2x[/B]

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2. We've got 2 algebraic expressions here. Let's take them in parts. Left side algebraic expression: twice the difference of a number and 3 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]difference[/I] means we subtract 3 from the variable x [*]x - 3 [*]Twice this difference means we multiply (x - 3) by 2 [*]2(x - 3) [/LIST] Right side algebraic expression: 3 times the sum of a number and 2 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]sum[/I] means we add 2 to the variable x [*]x + 2 [*]3 times the sum means we multiply (x + 2) by 3 [*]3(x + 2) [/LIST] Now, we have both algebraic expressions, the problem says [I]is equal to[/I] This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer [B]2(x - 3) = 3(x + 2)[/B]

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8 Take this algebraic expression in pieces. Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The difference of this number and 55 means we subtract 55 from x x - 55 Twice the difference means we multiply x - 55 by 2 2(x - 55) Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 8 means we add 8 to x x + 8 3 times the sum means we multiply x + 8 by 3 3(x + 8) Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side: [B]2(x - 55) = 3(x + 8)[/B]

seven plus x 7 + x Twice the quantity of seven plus x 2(7 + x) Difference of x and seven x - 7 The phrase [I]is the same as[/I] means equal to. This is our algebraic expression: [B]2(7 + x) = x - 7 [/B] If the problem asks you to solve for x, distribute 2 on the left side: 14 + 2x = x - 7 Subtract x from the right side 14 + x = -7 Subtract 14 from each side [B]x = -21[/B]

[SIZE=6]Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number. The phrase [/SIZE][I][SIZE=7]a number[/SIZE][/I][SIZE=6] means an arbitrary variable, let's call it x. The sum of a number and 6 means we add 6 to x: x + 6 Twice the sum of a number and 6 means we multiply x + 6 by 2: 2(x + 6) the difference of the number and 3 means we subtract 3 from x x - 3 three times the difference of the number and 3 means we multiply x - 3 by 3: 3(x- 3) The word [I]is[/I] means we set 2(x + 6) equal to 3(x - 3) 2(x + 6) = 3(x - 3) Use the distributive property to multiply through: 2x + 12 = 3x - 9 Subtract 2x from each side: 2x - 2x + 12 = 3x - 2x - 9 x - 9 = 12 Add 9 to each side: x - 9 + 9 = 12 + 9 x = [B]21[/B] [B][/B] [B][MEDIA=youtube]CeZl_oZnSiw[/MEDIA][/B][/SIZE]

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour? Set up two equations: (1) 10x + 5y = 1225 (2) x + y = 170 Rearrange (2) x = 170 - y Substitute that into (1) 10(170 - y) + 5y = 1225 1700 - 10y + 5y = 1225 1700 - 5y = 1225 Move 5y to the other side 5y + 1225 = 1700 Subtract 1225 from each side 5y =475 Divide each side by 5 [B]y = 95[/B] Which means x = 170 - 95, [B]x = 75[/B]

Two numbers have a sum of 20. If one number is p, express the other in terms of p. If the sum is 20 and one number is p, then let the other number be q. We have: p + q = 20 We want q, so we subtract p from each side: [B]q = 20 - p[/B]

Let the numbers be x and y. Set up our givens: [LIST=1] [*]x + y = 83 [*]x - y = 17 [/LIST] [U]Add equation (1) to equation (2)[/U] x + x + y - y = 83 + 17 [U]The y-terms cancel out:[/U] 2x = 100 [U]Divide each side by 2:[/U] 2x/2= 100/2 x = [B]50[/B] [U] Plug x = 50 into equation (1)[/U] 50 + y = 83 [U]Subtract 50 from each side:[/U] 50 - 50 + y = 83 - 50 [U]Cancel the 50 on the left side:[/U] y = [B]33 [/B] So our two numbers (x, y) = (33, 50) [MEDIA=youtube]jajO043ChUM[/MEDIA]

Two years of local internet service costs 685, including the installation fee of 85. What is the monthly fee? Subtract the installation fee of 85 from the total cost of 685 to get the service cost only: 685 - 85 = 600 Now, divide that by 24 months in 2 years to get a per month fee 600/24 = [B]25 per month[/B]

Tyler has a meal account with $1200 in it to start the school year. Each week he spends $21 on food a.) write an equation that relates the amount in the account (a) with the number of (w) weeks b.) How many weeks will it take until Tyler runs out of money? [U]Part a) where w is the number of weeks[/U] a = Initial account value - weekly spend * w ([I]we subtract because Tyler spends)[/I] a = [B]1200 - 21w [/B] [U]Part b)[/U] We want to know the number of weeks it takes where a = 0. So we have: 1200 - 21w = 0 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-21w%3D0&pl=Solve']type this equation into our search engine[/URL] and we get: w = 57.14 weeks The problem asks for when he runs out of money, so we round up to [B]58 whole weeks[/B]

66 decreased by d means we subtract: 66 - d v equals means we set our entire expression equal to v [B]66 - d = v[/B]

V − E + F = 2 for e To solve this literal equation, we want to isolate e. Add E to both sides: V − E + F + E = 2 + E The E's cancel on the left side, so we have: V + F = 2 + E Subtract 2 from each side: V + F - 2 = 2 + E + 2 The 2's cancel on the right side, so we have: E = [B]V + F - 2[/B]

Free Vectors Calculator - Given 2 vectors A and B, this calculates:
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, proj_BA and and the vector component of A orthogonal to B → A - proj_BA
Also calculates the horizontal component and vertical component of a 2-D vector.

Video store movie rental plans. Plan A 25 membership fee plus 1.25 for movie. Plan B 40 for unlimited rentals. What number of movies rentals is plan B less than plan A? Let x equal the number of movies rented and C the cost for rentals Plan A: C = 1.25x + 25 Plan B: C = 40 Set up the inequality: 1.25x + 25 > 40 Subtract 25 from each side: 1.25x > 15 Divide each side of the inequality by 1.25 x > 12 So [B]13[/B] rentals or more make Plan B less than Plan A.

vw^2+y=x for w This is an algebraic expression. Subtract y from each side: vw^2 + y - y = x - y The y's cancel on the left side, so we're left with: vw^2 = x - y Divide each side by v w^2 = (x - y)/v Take the square root of each side: w = [B]Sqrt((x - y)/v)[/B]

[QUOTE="Jahn, post: 78, member: 5"]Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute. After how many minutes are there equal volumes of water in the 2 tanks? Write an equation and solve it.[/QUOTE] Tank A: V = 200 - 2x Tank B: V = 100 - 0.5x Where x is the number of minutes passed. Set them equal to each other 200 - 2x = 100 - 0.5x Subtract 100 from each side: 100 - 2x = -0.5x Add 2x to each side: 1.5x = 100 Divide each side of the equation by x: x = 66.66666667

Wendy is paid $7.50 per hour plus a bonus of $80 each week. Last week Wendy earned $312.50. How many hours did Wendy work last week? Setup the earnings equation with h hours: 7.5h + 80 = 312.50 Solve for [I]h[/I] in the equation 7.5h + 80 = 312.50 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 80 and 312.50. To do that, we subtract 80 from both sides 7.5h + 80 - 80 = 312.50 - 80 [SIZE=5][B]Step 2: Cancel 80 on the left side:[/B][/SIZE] 7.5h = 232.5 [SIZE=5][B]Step 3: Divide each side of the equation by 7.5[/B][/SIZE] 7.5h/7.5 = 232.5/7.5 h = [B]31 [URL='https://www.mathcelebrity.com/1unk.php?num=7.5h%2B80%3D312.50&pl=Solve']Source[/URL][/B]

what integer is tripled when 9 is added to 3 fourths of it? Let the integer be n. Tripling an integer means multiplying it by 3. We're given: 3n = 3n/4 + 9 Since 3 = 12/4, we have: 12n/4 = 3n/4 + 9 Subtract 3n/4 from each side: 9n/4 = 9 [URL='https://www.mathcelebrity.com/prop.php?num1=9n&num2=9&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this equation into the search engine[/URL], we get: [B]n = 4[/B]

Answer Choices: A. 6 B. 1/2 C. 1/3 D. 1/4 [U]Multiply through by 6:[/U] 2 * 6x/3 + 6/6 = 6/3 4x + 1 = 2 [U]Subtract 1 from each side:[/U] 4x + 1 - 1 = 2 - 1 4x = 1 [U]Divide each side by 4:[/U] 4x/4 = 1/4 x = [B]1/4[/B] [MEDIA=youtube]jywMlPs3c2w[/MEDIA]

What number when multiplied by four exceeds itself by 42? Let the number be n. We have: 4n = n + 42 Subtract n from each side: 3n = 42 Divide each side by 3 [B]n = 14[/B]

What pair of consecutive integers gives the following: 7 times the smaller is less than 6 times the larger? Let x and y be consecutive integers, where y = x + 1 We have 7x < 6y as our inequality. Substituting x, y = x + 1, we have: 7x < 6(x + 1) 7x < 6x + 6 Subtracting x from each side, we have: x < 6, so y = 6 + 1 = 7 (x, y) = (6, 7)

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512 We set up an arbitrary number x. Subtracted from is written as -9876 - x The phrase [I]to obtain[/I] means an equation, so we set -9876 - x equal to -9512 -9876 - x = -9512 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=-9876-x%3D-9512&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]364[/B]

A certain number means an arbitrary variable, let's call it x x 3 times x 3x 20 is subtracted from 3 time x 3x - 20 The result is means equal to, so we set 3x - 20 equal to 43 for our algebraic expression [B]3x - 20 = 43 [/B] If you need to solve this, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-20%3D43&pl=Solve']equation calculator[/URL]: [B]x = 21[/B]

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution. Let the number be n. Square of a number: n^2 28 is subtracted from the square of a number: n^2 - 28 3 times the number: 3n [I]The result is[/I] mean an equation, so we set n^2 - 28 = 3n n^2 - 28 = 3n Subtract 3n from each side: n^2 - 3n - 28 = 3n - 3n The right side cancels to 0, so we have: n^2 - 3n - 28 = 0 This is a quadratic equation in standard form, so we [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-28%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']use our quadratic calculator[/URL] to solve: We get two solutions for n: n = (-4, 7) The question asks for the negative solution, so our answer is: [B]n = -4[/B]

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 integers. What is the difference of the product minus the sum? Let the 3 consecutive positive integers be: [LIST=1] [*]x [*]x + 1 [*]x + 2 [/LIST] The product is: x(x + 1)(x + 2) The sum is: x + x + 1 + x + 2 = 3x + 3 We're told the product is equivalent to: x(x + 1)(x + 2) = 16(3x + 3) x(x + 1)(x + 2) = 16 * 3(x + 1) Divide each side by (x + 1) x(x + 2) = 48 x^2 + 2x = 48 x^2 + 2x - 48 = 0 Now subtract the sum from the product: x^2 + 2x - 48 - (3x + 3) [B]x^2 - x - 51[/B]

When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution. Let the number be n. We have: n^2 - 4 = 3n Subtract 3n from each side: n^2 - 3n - 4 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Typing this quadratic equation into the search engine[/URL], we get: n = (-1, 4) The problem asks for the positive solution, so we get [B]n = 4[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x". 4 times a number, increased by 40, means we multiply 4 times x, and then add 40 4x + 40 100 decreased by the number means we subtract x from 100 100 - x The problem tells us both of these expressions are the same, so we set them equal to each other: 4x + 40 = 100 - x Add x to each side: 4x + x + 40 = 100 - x + x The x's cancel on the right side, so we have: 5x + 40 = 100 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 times a number means we multiply x by 4: 4x Increased by 40 means we add 40 to 4x: 4x + 40 100 decreased by the number means we subtract x from 100: 100 - x The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x 4x + 40 = 100 - x Solve for [I]x[/I] in the equation 4x + 40 = 100 - x [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4x and -x. To do that, we add x to both sides 4x + 40 + x = -x + 100 + x [SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE] 5x + 40 = 100 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 40 and 100. To do that, we subtract 40 from both sides 5x + 40 - 40 = 100 - 40 [SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE] 5x = 60 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5x/5 = 60/5 x = [B]12[/B] Check our work for x = 12: 4(12) + 40 ? 100 - 12 48 + 40 ? 100 - 12 88 = 88

When 54 is subtracted from the square of a number, the result is 3 times the number. This is an algebraic expression. Let's take it in parts. The phrase [I]a number[/I] means an arbitrary variable, let's call it "x". x Square the number, means raise it to the 2nd power: x^2 Subtract 54: x^2 - 54 The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3 [B]x^2 - 54 = 3[/B]

When 9 is subtracted from 5 times a number ,the result is 31 A number means an arbitrary variable, let's call it x. 5 times this number is written as 5x. 9 subtracted from this is written as 5x - 9 [I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression. Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at a speed of 750 meters per minute. The fox started to run away at a speed of 720 meters per minute. How soon will the dog catch the fox? The dog sits a position p. Distance = Rate x Time The dogs distance in minutes is D = 720t The fox sits at position p + 60 Distance = Rate x Time The fox's distance in minutes is D = 750t - 60 <-- Subtract 60 since the fox is already ahead 60 meters. We want to know when their distance (location) is the same. So we set both distance equations equal to each other: 720t = 750t - 60 [URL='https://www.mathcelebrity.com/1unk.php?num=720t%3D750t-60&pl=Solve']Using our equation calculator[/URL], we get [B]t = 2[/B]. Let's check our work: Dog's distance is 720(2) = 1440 Fox's distance is 750(2) - 60 = 1,440

When five people are playing a game called hearts, each person is dealt ten cards and the two remaining cards are put face down on a table. Because of the rules of the game, it is very important to know the probability of either of the two cards being a heart. What is the probability that at least one card is a heart? Probability that first card is not a heart is 3/4 since 4 suits in the deck, hearts are 1/4 of the deck. Since we don't replace cards, the probability of the next card drawn without a heart is (13*3 - 1)/51 = 38/51 Probability of both cards not being hearts is found by multiplying both individual probabilities: 3/4 * 38/51 = 114/204 Having at least one heart is found by subtracting this from 1 which is 204/204: 204/204 - 114/204 = 90/204 [URL='https://www.mathcelebrity.com/search.php?q=90%2F204&x=0&y=0']This reduces to[/URL] [B]15/34[/B]

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidentally left open. How long until the pool is completely filled? Set up unit fill rates per hour: [LIST] [*]1/4 of the pool is filled each hour [*]1/5 of the pool is drained away each hour [/LIST] The amount left over after an hour of filling minus draining is: [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Subtract']1/4 - 1/5[/URL] = 1/20 Therefore, it take [B]20 hours to fill the pool[/B]

When twice a number is reduced by 15 you get 95 what is the number? The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x [I]Twice[/I] x means we multiply x by 2 2x [I]Reduced by[/I] 15 means we subtract 15 2x - 15 [I]You get[/I] means equal to, as in an equation. Set 2x - 15 = 95 2x - 15 = 95 <-- This is our algebraic expression. [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D95&pl=Solve']Type 2x - 15 = 95 into the search engine[/URL] and we get [B]x = 55[/B].

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4? A) 6x + 2y = 15 B) 3x - y = 7 C) 2x - 3y = 6 D) x + 3y = 1 Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line. If we rearrange A) by subtracting 6x from each side, we get: 2y = -6x + 15 Divide each side by 2, we get: y = -3x + 15/2 This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].

William has 75 peppermints. Viana has p fewer peppermints than William Fewer means less, so we subtract to get Viana's total peppermints: [B]75 - p[/B]

Winnie earns an annual salary of $55,117. If she pays $3,715 a year in taxes and receives a paycheck every other week, how much does Winnie receive from each paycheck? Subtract the taxes to get Winnie's Total net pay: Total Net Pay = Annual Salary - Annual Taxes Total Net Pay =$55,117 - $3,715 Total Net Pay = $51,402 Now, if Winnie gets paid every other week, and there are 52 weeks in a year, then she gets paid 26 times. Calculate single paycheck amount Single Paycheck Amount = Total Net Pay / 26 payments Single Paycheck Amount = $51,402 / 26 Single Paycheck Amount = [B]$1,977[/B]

Write an algebraic expression for 8 multiplied by the result of u reduced by 11. u [I]reduced by[/I] 11 Reduced by means subtract 11 from u. So we have: u - 11 We multiply this expression by 8 to get our algebraic expression of: [B]8(u - 11)[/B]

Your answer is correct. Here is how I set up the profit equation where h is the hours worked and x is the supply cost: P(h) = 15.35h + x We know P(4) = 141.73 P(4) = 15.35(4) + x 141.73 = 15.35(4) + x Simplify 141.73 = 61.4 + x Subtract 61.4 from each side: [B]x = 80.33[/B]

wy - ma = ay/n for y Subtract ay/n from each side: wy - ma - ay/n = ay/n - ay/n wy - ma - ay/n = 0 Now add ma to each side: wy - ay/n = ma Factor out y: y(w - a/n) = ma Divide each side by (w - a/n) y = [B]ma/(w - a/n)[/B]

x + 8y/4 = 9y for x Step 1: Isolate x by subtracting 8y/4 from each side: x + 8y/4 - 8y/4 = 9y - 8y/4 Cancel 8y/4 on the left side: x =[B] 9y - 8y/4 [MEDIA=youtube]5NLDNw_T8GU[/MEDIA][/B]

x add y, multiply by z then subtract d Take this algebraic expression in pieces: [LIST] [*]x add y: x + y [*]multiply by z: z(x + y) [*]Subtract d: [B]z(x + y) - d[/B] [/LIST]

X divide by 6 subtract by 1 x divide by 6 x/6 subtract by 1 [B]x/6 - 1[/B]

x plus y times x minus y Plus means we add. Minus means we subtract. So we have: [B](x + y)(x - y)[/B]

x tripled less two is 5 x tripled means we multiply x by 3 3x Less two means we subtract 2 from 3x 3x - 2 [I]Is[/I] means equal to, so we set 3x - 2 equal to 5 [B]3x - 2 = 5[/B] [B][/B] To solve this equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-2%3D5&pl=Solve']equation solver[/URL].

(X+y)/3=5 for x Cross multiply: x + y = 15 Subtract y from each side: [B]x = 15 - y[/B]

x/y + 9 = n for x Subtract 9 from each side to isolate the x term: x/y + 9 - 9 = n - 9 Cancel the 9's on the left side and we get: x/y = n - 9 Because we have a fraction on the left side, we can cross multiply the denominator y by n - 9 [B]x =[/B] [B]y(n - 9)[/B]

x/y + 9 = n for y First, subtract 9 from each side to isolate the y term: x/y + 9 - 9 = n - 9 Cancel the 9's on the left side, and we get: x/y = n - 9 Cross multiply: x = y(n - 9) Divide each side by (n - 9): x/(n - 9) = y(n - 9)/(n - 9) Cancel the (n - 9) on the right side, and we get: y = [B]x/(n - 9)[/B]

y minus 10 is equal to the product of y and 8. Take this algebraic expression in 3 parts: Part 1: y minus 10 Subtract 10 from the variable y y - 10 Part 2: The product of y and 8 We multiply 8 by the variable y 8y Part 3: The phrase [I]is equal to[/I] means an equation, so we set y - 10 equal to 8y [B]y - 10 = 8y[/B]

Multiply each side by 2 to isolate y. y +2c = 2d Subtract 2c from each side of the equation: y = 2d - 2c This can also be written y = 2(d - c)

Yael worked out at a gym for 2 hours. Her workout consisted of stretching for 21 minutes,jogging for 45 minutes, and lifting weights for the remaining amount of time. What percentage of Yael’s workout was spent lifting weights? Each hour is 60 minutes, so we have 2 * 60 = 120 minutes of workout time for Yael. We subtract off the stretching and jogging time to get the time Yael lifted weights: 120 - 21 - 45 = 54 minutes

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a discount coupon for $7 off. What are the possible numbers of hours Yolanda could rent the boat? A few things to build this problem: [LIST=1] [*]Discount subtracts from our total [*]Cost = Hourly rate * hours [*]Less than means an inequality using the < sign [/LIST] Our inequality is: 8h - 7 < 41 To solve this inequality for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-7%3C41&pl=Solve']type it in our math engine[/URL] and we get: h < [B]6[/B]

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $15 each and you paid $6.50 a piece plus a $50 set-up fee and $25 for shipping. How many shirts do you have to sell to break even? Round to the nearest whole number. [U]Step 1: Calculate Your Cost Function C(s) where s is the number of t-shirts[/U] C(s) = Cost per Shirt * (s) Shirts + Set-up Fee + Shipping C(s) = $6.50s + $50 + $25 C(s) = $6.50s + 75 [U]Step 2: Calculate Your Revenue Function R(s) where s is the number of t-shirts[/U] R(s) = Price Per Shirt * (s) Shirts R(s) = $15s [U]Step 3: Calculate Break-Even Point[/U] Break Even is where Cost = Revenue. Set C(s) = R(s) $6.50s + 75 = $15s [U]Step 4: Subtract 6.5s from each side[/U] 8.50s = 75 [U]Step 5: Solve for s[/U] [URL='https://www.mathcelebrity.com/1unk.php?num=8.50s%3D75&pl=Solve']Run this through our equation calculator[/URL] to get s = 8.824. We round up to the next integer to get [B]s = 9[/B]. [B][URL='https://www.facebook.com/MathCelebrity/videos/10156751976078291/']FB Live Session[/URL][/B]

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen? Let n be our original number. Square the number means we raise n to the power of 2: n^2 Multiply the result by 2: 2n^2 And then add three: 2n^2 + 3 If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53: 2n^2 + 3 = 53 To solve for n, we subtract 3 from each side, to isolate the n term: 2n^2 + 3 - 3 = 53 - 3 Cancel the 3's on the left side, and we get: 2n^2 = 50 Divide each side of the equation by 2: 2n^2/2 = 50/2 Cancel the 2's, we get: n^2 = 25 Take the square root of 25 n = +-sqrt(25) n = +-5 We are told the number is positive, so we discard the negative square root and get: n = [B]5[/B]

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save 75 per week, and your friend saves 50 per week. When vacation time comes, you have 950, and your friend has 800. How much did you start with, and for how many weeks did you save? [U]Let w be the number of weeks. Set up two equations where s is the starting amount:[/U] (1) s + 75w =950 (2) s + 50w = 800 [U]Rearrange (1) into (3) to solve for s by subtracting 75w[/U] (3) s = 950 - 75w [U]Rearrange (2) into (4) to solve for s by subtracting 50w[/U] (4) s = 800 - 50w [U]Set (3) and (4) equal to each other so solve for w[/U] 950 - 75w = 800 - 50w [U]Add 75w to each side, and subtract 950 from each side:[/U] 25w = 150 [U]Divide each side by w[/U] [B]w = 6[/B] Now plug w = 6 into (3) s = 950 - 75(6) s = 950 - 450 [B]s = 500[/B]

You are comparing the costs of producing shoes at two different manufacturers. Company 1 charges $5 per pair of shoes plus a $650 flat fee. Company 2 charges $4 per pair of shoes plus a $700 flat fee. How many pairs of shoes are produced when the total costs for both companies are equal? Let s be the number of shoes. We have two equations: (1) C = 5s + 650 (2) C = 4s + 700 Set the costs equal to each other 5s + 650 = 4s + 700 Subtract 4s from each side s + 650 = 700 Subtract 650 from each side [B]s =50[/B]

You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company offers a salary of $330 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good? Let s be the sales and C be the weekly commission for each sales job. We have the following equations: [LIST=1] [*]C = 0.06s [*]C = 330 + 0.02s [/LIST] Set them equal to each other: 0.06s = 330 + 0.02s Subtract 0.02s from each side: 0.04s = 330 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.04s%3D330&pl=Solve']equation solver[/URL], we get [B]s = 8,250[/B]

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost? Subtract the cost of the magazine from what you spent: $25 - $5 = $20. If you spent $20 on 4 erasers, we divide 20/4 = [B]$5 per eraser[/B]

You can pay a daily entrance fee of $3 or purchase a membership for the 12 week summer season for $82 and pay only $1 per day to swim. How many days would you have to swim to make the membership worthwhile? Set up cost equations: Daily entrance fee: 3d where d is the number of days of membership Membership fee 82 + 1d Set them equal to each other 82 + 1d = 3d Subtract d from each side: 2d = 82 Divide each side by 2 [B]d = 41[/B]

You collect stamps. You give steven 21 stamps. At the end youbhave 3. How many stamps did you start with? You start with s stamps. s You give Steven 21. Giving means you subtract from your total: s - 21 You have 3 left s - 21 = 3 To solve this equation for s, we t[URL='https://www.mathcelebrity.com/1unk.php?num=s-21%3D3&pl=Solve']ype it in our math engine[/URL] and we get: s = [B]24[/B]

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject? Let m be the math problems and s be the science problems. We have two equations: (1) m + s = 42 (2) m = s + 10 Substitute (2) into (1) (s + 10) + s = 42 Combine like terms 2s + 10 = 42 Subtract 10 from each side 2s = 32 Divide each side by 2 [B]s = 16[/B] So that means m = 16 + 10 --> [B]m = 26 (m, s) = (26, 16)[/B]

You spend $91 shopping for new clothes. You spend $24 for a pair of jeans and 35$ for a pair of shoes. You also buy 4 shirts that cost d dollars. How much is each shirt? Subtract the cost of the jeans and shoes to get the cost of the shirts: Cost of shirts = Shopping Spend - Cost of Jeans - Cost of Shoes Cost of shirts = $91 - $24 - $35 Cost of shirts = $32 We're given the cost of each shirt is s, and we bought 4 shirts. Therefore, we have: 4s = 32 [URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D32&pl=Solve']Type this equation into the search engine[/URL], and we get the cost of each shirt s = [B]$8[/B]

Your brother has $2000 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to find how much he can spend for everything else. Let x be the amount your brother can spend. Subtracting the cost of the plane ticket from savings, we have: x <= 2000 - 637 [B]x <= 1,363[/B]

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase? Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations: [LIST=1] [*]c + f = 10 [*]c + 1.5f = 12.50 [/LIST] Rearrange equation 1 by subtracting f from both sides: [LIST=1] [*]c = 10 - f [*]c + 1.5f = 12.50 [/LIST] Substitute equation (1) into equation (2): 10 - f + 1.5f = 12.50 To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=10-f%2B1.5f%3D12.50&pl=Solve']type this equation into our search engine[/URL] and we get: [B]f = 5[/B] Now, substitute this f = 5 value back into modified equation (1) above: c = 10 - 5 [B]c = 5[/B]

z , subtract 5 then times by 3 Take this algebraic expression two parts: [LIST] [*]z subtract 5: z - 5 [*][I]Then times by 3[/I] means we multiply the expression z - 5 by 3 [/LIST] [B]3(z - 5)[/B]

z = (x + y)/mx; Solve for x Cross multiply: zmx = x + y Subtract x from each side zmx - x = y Factor out x x(zm - 1) = y Divide each side by zm - 1 x = y/(zm - 1) [MEDIA=youtube]ksxCS3YlCwY[/MEDIA]

z fewer than the difference of 5 and y Take this algebraic expression in parts: The difference of 5 and y means we subtract y from 5 5 - y z fewer than this difference means we subtract z from 5 - y [B]5 - y - z[/B]

z/w=x+z/x+y for z This is a literal equation. Let's isolate z on one side. Subtract z/x from each side. z/w - z/x = x + y Factor our z on the left side: z(1/w - 1/x) = x + y Divide each side by (1/w - 1/x) z = x + y/(1/w - 1/x) To remove reciprocals in the denominator, we rewrite 1/w - 1/x with a common denominator xw (x - w)/xw Then multiply x + y by the reciprocal z = [B](x + y)xw/(x - w)[/B]

z=m-x+y, for x This is a literal equation. Let's add subtract (m + y) from each side: z - (m + y) = m - x + y - (m + y) The m + y terms cancel on the right side, so we have: z - m - y = -x Multiply each side by -1 to isolate x: -1(z - m - y) = -(-x) x = [B]m + y - z[/B]

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x): [U]She subtracts 6 then multiplies the result by 5[/U] [LIST] [*]Subtract 6: x - 6 [*]Multiply the result by 5: 5(x - 6) [/LIST] [U]She subtracts 5 from the number then multiplying by 4[/U] [LIST] [*]Subtract 6: x - 5 [*]Multiply the result by 5: 4(x - 5) [/LIST] Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation: 5(x - 6) = 4(x - 5) Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get: x = [B]10[/B]

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