Question

EZ car rental charges $40 dollars a day plus $0.25 per mile. Ace Rent-A-Car charges $25 dollars a day plus $0.45 per mile. What number of miles results in the same costs as one day?

Answer 1

Find an expression for each Rental car company's charge in one day where x = the number of miles driven.
EZ car rental: 0.25x + 40
Ace Rent-a-car: 0.4x + 25

You want to find when the two expressions are equal, so set the two expressions equal:
0.25x + 40 = 0.40x + 25
Solve for x!

0.25x + 15 = 0.40x
15 = 0.15x
x = 15/0.15
x = 100

You can check by plugging the number back in:
0.25 (100) + 40 = 65
0.4 (100) + 25 = 65

Answer 2

75 miles.

Explanation:

Let x represent number of miles.

We have been given that EZ car rental charges $40 dollars a day plus $0.25 per mile. The total cost of renting a car for x miles would be
`0.25x+40`.

We are also told that Ace Rent-A-Car charges $25 dollars a day plus $0.45 per mile. The total cost of renting a car for x miles would be
`0.45x+25`.

To find the number of miles, when both companies will cost same, we will equate both expressions and solve for x.

`0.45x+25=0.25x+40`

`0.45x-0.25x+25=0.25x-0.25x+40`

`0.20x+25=40`

`0.20x+25-25=40-25`

`0.20x=15`

`(0.20x)/(0.20)=(15)/(0.20)`

`x=75`

Therefore, 75 miles results in the same costs as one day.