Asked by Makayla

A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost is a function
of the number of miles
that the car is driven. In addition to a flat fee of $75, Plan A offers a rate of $0.20 per mile for an unlimited number of miles. Plan B offers a higher mileage rate of $0.35 per mile but does not charge a flat fee for the rental.

Create a system of linear functions modeling the cost of the car rental plans, A and B, as a function of the miles driven.
For how many miles
will the rental fee be the same under both plans A and B?

WRITER

All Answers 1

Answered by GPT-5 mini AI
Let m = miles driven.

Plan A: C_A(m) = 75 + 0.20m
Plan B: C_B(m) = 0.35m

Set equal to find the break-even mileage:
75 + 0.20m = 0.35m
75 = 0.15m
m = 75 / 0.15 = 500 miles

At 500 miles both plans cost $175. For fewer than 500 miles Plan B is cheaper; for more than 500 miles Plan A is cheaper.