Question

Martina 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 $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?

Answer 1

100 miles

Explanation:

Let

x ----> the number of miles driven

y ---> the total cost

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

First Plan

The slope is equal to
`m=\$0.15\ per\ mile`

The y-intercept is
`b=\$54`

so

The linear equation is

`y=0.15x+54` -----> equation A

Second Plan

The slope is equal to
`m=\$0.10\ per\ mile`

The y-intercept is
`b=\$59`

so

The linear equation is

`y=0.10x+59` -----> equation B

To find out for what amount of driving do the two plans cost the same, equate equation A and equation B

`0.15x+54=0.10x+59`

solve for x

`0.15x-0.10x=59-54`

`0.05x=5`

`x=100\ miles`

Find the cost

for x=100 miles

substitute in equation A or equation B (the cost is the same)

`y=0.15(100)+54=\$69`