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.

Question

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

Hi, Javier.

Okay, so we need to find the cost of each plan with respect to the number of miles driven.

The first plan has an initial fee of $48 and then $0.15/mile driven.

Therefore the cost in terms of x miles driven is:

48.00 + 0.15x

The second plan has an initial fee of $53 and $0.10/mile driven.

Therefore, the cost in terms of x miles driven is:

53 + 0.10x

Now, to find when the two costs are the same, set them equal to each other. This will give us the solution for the number of miles driven (x) in which the two costs are equal.

48.00 + 0.15x = 53.00 + 0.10x

Now, isolate x on one side:

48.00 + (0.15x - 0.10x) = 53.00 + (0.10x - 0.10x)

48.00 + 0.05x = 53.00

(48.00-48.00) + 0.05x = (53.00-48.00)

0.05x = 5.00

0.05x/0.05 = 5.00/0.05

x = 100

S0 the cost is the same when she drives 100 miles.

To find the cost for 100 miles, simply insert 100 into each expression.

The first plan is $48.00 + $0.15(100) = $48.00 + $15.00 = $63.00

The second plan is $53.00 + $0.10(100) = $53.00 + $10.00 = $63.00

This proves that we have the correct answer for the number of miles driven to give equal costs.

Also, this tells us that it costs $63.00 to drive 100 miles.