Modeling Real-Life Situations with Linear Equations

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) of renting a car for x miles. How much would it cost to drive 150 miles?

• $100

• $60

• $80

• $120

A store sells notebooks for $2 each and pens for $1 each. If a student buys a total of 10 items and spends $16, write a system of equations to represent the situation. How many notebooks and pens did the student buy?

• 5 notebooks and 5 pens

• 6 notebooks and 4 pens

• 4 notebooks and 6 pens

• 7 notebooks and 3 pens

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 meters more than twice the width. If the perimeter of the garden is 36 meters, write a linear equation to find the dimensions of the garden. What are the length and width?

• Length: 10 meters, Width: 8 meters

• Length: 13 meters, Width: 5 meters

• Length: 12 meters, Width: 4 meters

• Length: 15 meters, Width: 6 meters

A phone plan costs $30 per month plus $0.10 per text message sent. If a customer’s bill is $50 one month, how many text messages did they send? Write an equation to model this situation and interpret the solution.

• 100

• 150

• 200

• 250

A school is organizing a field trip. The cost per student is $25, and there is a fixed cost of $200 for the bus. Write a linear equation to represent the total cost (C) for s students. How much will it cost for 30 students?

• $1,200

• $800

• $600

• $950

A factory produces 500 toys in 8 hours. If the production rate is constant, write a linear equation to model the number of toys produced (T) in h hours. How many toys are produced in 12 hours?

• 600 toys

• 800 toys

• 500 toys

• 750 toys

A local bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 15 items and spends $36, write a system of equations to find out how many cupcakes and cookies were purchased. What is the solution?

• 6 cupcakes and 9 cookies

• 5 cupcakes and 10 cookies

• 4 cupcakes and 11 cookies

• 7 cupcakes and 8 cookies

A swimming pool is being filled with water at a rate of 5 gallons per minute. If the pool can hold 1,000 gallons, write a linear equation to model the time (t) it takes to fill the pool. How long will it take to fill the pool?

• 300 minutes

• 250 minutes

• 200 minutes

• 150 minutes

A concert venue has a seating capacity of 1,200. If tickets are sold for $20 each, write a linear equation to represent the total revenue (R) from selling t tickets. How much revenue is generated if 800 tickets are sold?

• $16,000

• $8,000

• $12,000

• $20,000

A bike rental shop charges a $15 fee plus $5 for each hour a bike is rented. Write a linear equation to represent the total cost (C) for renting a bike for h hours. If a customer pays $40, how many hours did they rent the bike?

• 3 hours

• 5 hours

• 7 hours

• 10 hours