Solving Substitution Word Problems: Variables & Equations

A school is planning a field trip. The cost per student is $15, and the total cost for the trip is $300. Let x be the number of students. Set up an equation to find how many students are going on the trip.

• 20

• 30

• 15

• 25

Maria has twice as many apples as John. If John has x apples, write an equation to express the total number of apples Maria has. How many apples does Maria have if John has 5 apples?

• 8

• 15

• 10

• 12

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If the total cost for a rental is $70, how many miles did the car travel? Let y be the number of miles driven and set up the equation accordingly.

• 50 miles

• 75 miles

• 120 miles

• 100 miles

In a class, the number of boys is 3 more than twice the number of girls. If g represents the number of girls, write an equation to express the number of boys. How many boys are there if there are 4 girls?

• 8

• 11

• 12

• 10

A bookstore sells novels for $12 each and textbooks for $20 each. If a customer buys a total of 5 books for $72, let n be the number of novels and t be the number of textbooks. Set up the equations to find how many of each type of book was purchased.

• 3 novels and 2 textbooks

• 4 novels and 1 textbook

• 1 novel and 4 textbooks

• 2 novels and 3 textbooks

A gardener is planting flowers in two types of pots. The small pots hold 3 flowers each, and the large pots hold 5 flowers each. If the total number of flowers is 24, let s be the number of small pots and l be the number of large pots. Write the equation to find the number of each type of pot used.

• 5s + 2l = 24

• 3s + 5l = 24

• 4s + 3l = 24

• 2s + 4l = 24

A movie theater sells adult tickets for $10 and child tickets for $6. If a family buys a total of 8 tickets for $54, let a be the number of adult tickets and c be the number of child tickets. Set up the equations to determine how many of each type of ticket was purchased.

• 2 adult tickets and 6 child tickets

• 3 adult tickets and 5 child tickets

• 4 adult tickets and 4 child tickets

• 1 adult ticket and 7 child tickets

A recipe requires 2 cups of flour and 3 cups of sugar. If you want to make a batch that uses 12 cups of flour, how many cups of sugar will you need? Let f be the cups of flour and s be the cups of sugar. Write the equation and solve for s.

• 24 cups of sugar

• 12 cups of sugar

• 18 cups of sugar

• 6 cups of sugar

A bike rental shop charges a $15 fee plus $5 for each hour rented. If a customer pays $40, how many hours did they rent the bike? Let h be the number of hours rented and set up the equation to find h.

• 3

• 5

• 4

• 6

In a school, the number of students in the 8th grade is 50 more than the number of students in the 7th grade. If s represents the number of 7th graders, write an equation to express the number of 8th graders. How many 8th graders are there if there are 100 7th graders?

• 200

• 75

• 100

• 150