Mathematics: 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?

Martina will rent a car for the weekend. she can

khliyahmccaskil

13.01.2022

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 $b=\$54$

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 $b=\$59$

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)

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

0,0(0 оценок)