Question

You are considering renting a car from two different rental companies. Proxy car rental company charges. $0.32 per mile plus an $18 surcharge. YourPal rental company charges $0.36 per mile plus a $12 surcharge.
For what distance is the price the same for both companies?

Answer 1

Let y = total charge for a car rental and x = miles driven
Proxy car equation: y = 0.32x + 18
YourPal equation: y = 0.36x + 12

Set equations right sides equal to each other... meaning their cost, y, are equal
0.32x + 18 = 0.36x + 12
18 = 0.04x + 12  (subtract 0.32x from both sides of the equation)
6 = 0.04x            (subtract 12 from both sides of the equation)
150 = x               (divide both sides of the equation by 0.04)
ANSWER: 150 miles