Question

Keisha will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0.15 per mile driven. The second plan has an initial fee of $53 and costs an additional $0.13 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?

Answer 1

650 miles has to driven before the plans cost the same

When the two plans cost the same, the cost is $ 137.5

Solution:

Given that, Keisha can choose one of two plans

Let "n" be the number of miles driven

For Keisha 1st Plan:

The first plan has an initial fee of $40 and costs an additional $0.15 per mile driven

Therefore,

Cost of plan 1 = 40 + (0.15)n

For Keisha 2nd plan:

The second plan has an initial fee of $53 and costs an additional $0.13 per mile driven

Cost of plan 2 = 53 + (0.13)n

To find out the number of miles where the two plans cost the same set the two expressions equal to each other and solve for n

40 + 0.15n = 53 + 0.13n

0.15n - 0.13n = 53 - 40

0.02n = 13

n = 650

Thus 650 miles has to driven before the plans cost the same

Substitute 650 in any one of equations

40 + 0.15n = 40 + (0.15)(650) = 40 + 97.5 = 137.5

When the two plans cost the same, the cost is $ 137.5