Question

Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $48 and costs an additional $0.15 per mile driven.

The second plan has an initial fee of $53 and costs an additional $0.10 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

100 miles

Cost = $63

Explanation:

Let us assume that the distance driven for both plans when they both equal in cost is X miles

Plan 1

Cost = 48 + 0.15X

Plan2

Cost = 53 + 0.1X

If they are both equal then

48 + 0.15X = 53 + 0.10X

Collecting like terms

0.15X - 0.10X = 53 - 48

0.05X = 5

X 5/0.05 = 100 miles

Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63

Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63