Question

Kelko will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57 and cost an additional $0.08 per mile driven. The second plan has an initial fee of $50 and costs and additional $0.10 per mile driven.

Answer 1

Questions (contd)

(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:

(a) 100 miles

(b) $65

Explanation:

Given

Plan 1:

`Initial\ Fee = \$57`

`Additional = \$0.08` per mile

Plan 2:

`Initial\ Fee = \$50`

`Additional = \$0.10` per mile

Solving (a): Number of miles when both plans are equal

Represent the distance with x and the cost with y

So:

Plan 1:

`y = 57 + 0.08 * x`

Plan 2:

`y = 50 + 0.10 * x`

To solve (a), we equate both plans together; i.e.

`y = y`

`57 + 0.08x = 50 + 0.10x`

Collect Like Terms

`0.08x - 0.10x= 50 - 57`

`-0.02x= -2`

Solve for x

`x = -2/-0.02`

`x = 100`

Hence, 100 mile would cost both plans the same

Solving (b): Cost when both plans are the same:

In this case, we simply substitute 100 for x in any of the y equation.

`y = 57 + 0.08 * x`

`y = 57 + 0.08 * 100`

`y = 57 + 8`

`y = 65`

Hence, the amount is $65