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

Answer:

100 miles

Step-by-step 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)

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