how to solve algebra word problems

The length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, what are the dimensions? Set up 2 equations given P = 2l + 2w: l = 2w - 6 2l + 2w = 60 Substitute (1) into (2) for l: 2(2w - 6) + 2w = 60 4w - 12 + 2w = 60 6w - 12 = 60 To solve for w, type this into our...

The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensions? We're given 2 equations: l = 3w P = 80 = 2l + 2w = 80 Substitute (1) into (2) for l: 2(3w) + 2w = 80 6w + 2w = 80 8w = 80 Divide each side by 8: 8w/8 = 80/8 w = 10 Substitute w = 10 into...

Let x be the larger number. Let y be the smaller number. We're given two equations: x + y = 231 x = 2y Substitute (2) into (1) for x: 2y + y = 231 3y = 231 Type this into our math solver and get y = 77 This means x is: x = 2(77) x = 154

Let m be Mary's age Let j be John's age j = 2m

The phrase a number means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. Twice a number: 2x decreased by eight 2x - 8 is means equal to. Set 2x - 8 equal to zero for our algebraic expression: 2x - 8 = 0 If the problem asks you to solve for x, add 8 to...

The sum of two y and the quantity of three plus y plus twice the quantity two y minus two equals fifteen The sum of two y and the quantity of three plus y 2y + (3 + y) twice the quantity two y minus two 2(2y - 2) The sum of two y and the quantity of three plus y plus twice the quantity two y...

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

two y and six 2y + 6 Twice the quantity: 2(2y + 6)

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

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: 2y + 3 = 3y - 1 If the problem asks you to solve for y, subtract 2y from each side: 3 = y - 1 Add 1 to each side: y = 4

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

The phrase a number 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 ten added to twice a number 2x + 10 The phrase is the same as means equal to. Set 25 equal to 2x + 10 to get our algebraic expression 25...

The phrase a number 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: 5x - 16...

The phrase a number means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. Four times a number: 4x nine more than four times a numbrer 4x + 9 The phrase is means equal to. We set 4x + 9 equal to 25 as our algebraic expression: 4x + 9 = 25 If the problem...

The phrase a number 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 is means equal to. We set 2x - 4 equal to 20 for our algebraic expression: 2x - 4 = 20 If the problem...

The phrase a number means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. One-half a number means we divide x by2: x/2 The word is means equal to. We set x/2 equal to 50 for our algebraic expression x/2 = 50 If the problem asks us to solve for x, we...

The phrase a number means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. 3 times a number: 3x The sum of three times a number and twelve means we add 12 to 3x: 3x + 12

The phrase a number 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: 5x - 4

The phrase a number 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: 2x - 6

the quantity y plus two y + 2 the quantity y plus two divided by four (y +2)/4 Eight times the quantity y plus two divided by four 8(y +2)/4 8/4 = 2, so we have: 2(y +2) or 2y + 4