Keiko will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $54 and costs an additional $0.19 per mile driven.

Question

The second plan has an initial fee of $59 and costs an additional $0.14 per mile driven. 

(a) For what amount of driving do the two plans cost the same?

(b) What is the cost when the two plans cost the same?

Answer 1

Cost of Plan 1 is 54+.19x

Cost of Plan 2 is 59+.14x

where x is the number of miles driven. 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 x

.19x +54 = .14x +59

.05x= 5

x=100 miles

Can use either expression to determine cost at 100 miles as this is the point at which they are equal

.19(100) + 54= 19 +54 = 73 or

.14(100) + 59= 14 +59 = 73