Question

Prestige car rentals charge $44 per day plus 6 cents per mile to rent a mid sized vehicle. Gateway auto charges $35 per day plus 9 cents per mile for the same car . For what number of miles both companies charge the same price

Answer 1

300 miles

Explanation:

Let

x ----> the number of miles

y ----> the total cost for rent a car

we know that

The equation of the line in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate

b is the y-intercept or initial value

Prestige car rentals

we have that

The slope is equal to
`m=\$0.06\ per\ mile`

The y-intercept is
`b=\$44`

therefore

`y=0.06x+44` -----> equation A

Gateway auto

we have that

The slope is equal to
`m=\$0.09\ per\ mile`

The y-intercept is
`b=\$35`

therefore

`y=0.09x+35` -----> equation B

For what number of miles both companies charge the same price>

Equate equation A and equation B

`0.09x+35=0.06x+44`

solve for x

`0.09x-0.06x=44-35\\0.03x=9\\x=300\ miles`