Linear Relationships: Word Problems & Rate of Change

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an equation to represent the total cost (C) as a function of miles driven (m). What is the rate of change in this scenario?

• C = 50 + 0.20m; Rate of change = $0.20 per mile.

• C = 50 + 0.50m; Rate of change = $0.50 per mile.

• C = 50m + 0.20; Rate of change = $50 per mile.

• C = 0.20 + 50m; Rate of change = $50 per mile.

Maria is saving money to buy a new bike. She saves $15 each week. Write an equation to represent her total savings (S) after w weeks. How much will she have saved after 8 weeks?

• 150

• 75

• 90

• 120

A gardener is planting flowers in rows. Each row contains 5 flowers. Write an equation to represent the total number of flowers (F) in r rows. What is the rate of change of flowers per row?

• F = 5r; Rate of change = 5

• F = 5r + 2; Rate of change = 5

• F = 3r; Rate of change = 3

• F = 10r; Rate of change = 10

A phone company offers a plan that costs $30 per month plus $0.10 per text message. Write an equation for the total cost (C) based on the number of text messages (t) sent. What is the rate of change?

• C = 30t + 0.10; Rate of change = 30

• C = 30 + 0.05t; Rate of change = 0.05

• C = 30 + 0.20t; Rate of change = 0.20

• C = 30 + 0.10t; Rate of change = 0.10

A train travels at a constant speed of 60 miles per hour. Write an equation to represent the distance (D) traveled after t hours. How far will the train travel in 3 hours?

• 240 miles

• 120 miles

• 150 miles

• 180 miles

A bookstore sells notebooks for $2 each. Write an equation to represent the total cost (C) for buying n notebooks. What is the rate of change in cost per notebook?

• C = n; Rate of change = 1

• C = 3n; Rate of change = 3

• C = 2n; Rate of change = 2

• C = 2n + 1; Rate of change = 2

A factory produces 100 toys per hour. Write an equation to represent the total number of toys (T) produced after h hours. How many toys will be produced in 5 hours?

• 500

• 700

• 600

• 400

A swimming pool is being filled at a rate of 200 gallons per hour. Write an equation to represent the total volume of water (V) in gallons after t hours. How much water will be in the pool after 4 hours?

• 1000 gallons

• 400 gallons

• 600 gallons

• 800 gallons

A taxi charges a base fare of $3 plus $2 for each mile driven. Write an equation for the total fare (F) based on the number of miles (m) driven. What is the rate of change in fare per mile?

• F = 3 + 3m; Rate of change = 3

• F = 3 + 2m; Rate of change = 2

• F = 3 + m; Rate of change = 1

• F = 2 + 3m; Rate of change = 3

A school is organizing a field trip. The cost per student is $25, and there are 30 students attending. Write an equation to represent the total cost (C) for s students. What is the total cost for 30 students?

• The total cost for 30 students is $750.

• The total cost for 30 students is $900.

• The total cost for 30 students is $600.

• The total cost for 30 students is $500.