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...
A local shop sold 499 hamburgers and cheese burgers. There were 51 fewer cheese burgers sold. How many hamburgers were sold?
Let h = number of hamburgers sold and c be the number of cheeseburgers sold.
We have two equations:
(1) c = h - 51
(2) c + h = 499
Substitute (1) into (2)
h - 51 + h =...
4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many teaspoons of vinegar?
Set up a proportion where x is the number of teaspoons of vinegar in the second scenario:
4/6 = 20/x
Plug that expression into the search engine to get
x = 30
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 = 83
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...
Let k = Katie's age and m = Mara's age.
We have 2 equations:
(1) k = 2m
(2) k + m = 24
Substitute (1) into (2)
(2m) + m = 24
Combine like terms:
3m = 24
Divide each side of the equation by 3 to isolate m
m = 8
If m = 8, substituting into (1) or (2), we get k = 16.
Company a charges $25 plus $0.10 a mile. Company b charges $20 plus $0.15 per mile. How far would you need to travel to get each charge to be the same?
Let x be the number of miles traveled
Company A charge: C = 25 + 0.10x
Company B charge: C = 20 + 0.15x
Set up an equation find out when the...
There are 4064 calories in 8 pints of strawberry ice cream. How many calories are there in each pint of strawberry ice cream?
Set up a proportion using x as the number of calories in 1 pint of ice cream.
4064/8 = x/1
Using our proportion calculator, we get:
x = 508
If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how many students do each have?
Let h = Mr. Hernandez's students and d = Mr. Daniels students.
We are given two equations:
(1) h = 5d
(2) d + h = 150
Substitute equation (1) into equation (2)
d +...
Let g = Gary's pets and a = Abe's pets.
We are given two equations:
(1) g = a - 3
(2) a + g = 15
Substitute (1) into (2)
a + (a - 3) = 15
Combine Like Terms:
2a - 3 = 15
Add 3 to each side:
2a = 18
Divide each side by 2 to isolate a:
a = 9 --> Abe has 9 pets
Substitute a = 9 into Equation...
The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
P = 2l + 2w
Since P = 120, we have:
(1) 2l + 2w = 120
We are also given:
(2) l = 3w - 6
Substitute equation (2) into equation (1)
2(3w - 6) + 2w =...
There are 32 female performers in a dance recital. The ratio of men to women is 3:8. How many men are in the dance recital?
3:8 = x:32
3/8 = x/32
Cross multiply:
8x = 96
Divide each side by 8
x = 12
Check our work:
12:32
Divide each part by 4
12/4 = 3 and 32/4 = 8 so we have 3:8 :)
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...
Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Carmen wants the total calorie count from the french...
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...
We need to find the unit cost, which is the cost of one unit of measurement.
The measurement unit is in pounds.
If it costs $11.25 for a 3 pound bag, how much is it per pound?
$11.25/3 = $3.75 per pound.