Question

Elizebeth loves road trips and last summer she took two. On her first trip she spent $226 on a rental car which she rented for 4days and traveled 350 miles. On her second trip she paid $52 for the rental car which she rented for 1 day and traveled 75 miles. The company she rents from charges a daily fee, plus an additional charge for each mile driven. How much did the company charge per day and per mile to rent the vehicle?

Answer 1

You may solve this problem using a system of equations. Let the daily fee be x and the amount charged per mile be y.

This makes the equation for the first road trip:
226 = 4x + 350y

and the equation for the second road trip:
52 = x + 75y

rendering the following system of equations:
226 = 4x + 350y
52 = x + 75y

To solve this system using the substitution method, first isolate x in the second equation.

52 = x + 75y
52 - 75y = x
x = 52 - 75y

Substitute 52 - 75y for x into the first equation and solve algebraically for y.

226 = 4x + 350y
226 = 4(52 - 75y) + 350y
226 = 208 - 300y + 350y
226 = 208 + 50y
18 = 50y
18/50 = y
9/25 = y
y = 9/25

Substitute 9/25 for y into either of the original equations and solve algebraically for x.

52 = x + 75y
52 = x + 75(9/25)
52 = x + 675/25
52 = x + 27
25 = x
x = 25

Answer:
The company charged a daily fee of $25 and a they charged $0.36 per mile to rent the vehicle.