Solving Systems of Equations in Word Problems

Practice Questions

ACT Math Test › Solving Systems of Equations in Word Problems

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1

Judy and Nancy participated in a walk-a-thon to raise money for charity. They combined for 42 total miles between them, with Judy walking twice as many miles as Nancy. How many miles did Nancy walk?

2

The snack bar at a certain lake sells slices of pizza in two varieties: vegetarian pizza costs $1.25 per slice, and pepperoni pizza costs $1.50 per slice. If the snack bar sold a total of 20 slices of pizza for a total of $28.25 on a particular day, how many more slices of pepperoni were sold than slices of vegetarian?

3

The formula above gives the monthly cost, , of running a food truck, where the driver works hours and gallons of gasoline are used for driving and operating the truck. If, in a particular month, it costs more than $3,500 to run the truck and no more than 220 gallons of gas were used, what is the minimum number of hours that the driver worked that month?

4

Jim spent $60 purchasing lattes and coffees for his coworkers. If lattes cost $6 and coffees cost $3, and Jim purchased two more coffees than lattes, how many total drinks did he purchase?

5

Blin and Alex raised a total of $240,000 for a charity. If Blin raised $60,000 more than Alex did, how much money did Blin raise?

6

Siblings Tamika and David tracked every hour they spent studying during a particular school year. Combined, they studied for a total of 932 hours, with Tamika studying for 28 more hours than her brother David did. How many hours did Tamika study?

7

A movie theater sold 120 tickets to the matinee showing of a popular children's movie, and 150 tickets to the evening showing. The theater sold the same number of adult tickets for each show, but for the evening show was just 20 children's tickets short of selling twice as many children's tickets as it did for the matinee. How many children's tickets were sold to the evening show?

8

Joanna has two dogs, Rover and Spot, who weigh a combined total of 87 pounds. If Rover weighs 9 pounds more than Spot, how many pounds does Spot weigh?

9

A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $160. The cost for 1 bat and 6 balls is $160, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $240 for the purchase?

10

An outdoor concert venue sells two types of tickets: balcony tickets cost $30 and main floor tickets cost $55. When the venue sells all 500 available tickets for a given show it earns a total of $20,000. How many main floor tickets does the venue offer for each show?

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