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?

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