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?

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

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