Question

George needs to rent a car for one day. He can rent a Cadillac from Gamma Car Rental for $30.39 per day plus 55 cents per mile. He can get the same car from Delta Car Rental for $50.31 per day plus 43 cents per mile. What number of miles results in the price for Gamma being equal to the price for Delta? Write your answer as a number only

Answer 1

Call the number of days 'd' and the number of miles 'm'.
(Original, eh ?)

Then the equation for Gamma's price is

                           Price-G = 30.39d + 0.55m

and the equation for Delta's price is

                            Price-D = 50.31d + 0.43m .

We're going to set the prices equal, and find out
what the number of miles is:

                       Price-G = Price-D.

        30.39d + 0.55m  = 50.31d + 0.43m .

Before we go any farther, I'm going to assume that both cases would be
one-day rentals.  My reasons:  ==> the solution for the number of miles
depends on how many days each car was rented for;  ==> even if both
cars are rented for the same number of days, the solution for the number
of miles depends on what that number of days is.

For 1-day rentals, d=1, and

                                        30.39 + 0.55m  =  50.31 + 0.43m .
Beautiful.  Here we go.
Subtract 0.43m
from each side:              30.39 + 0.12m  =  50.31

Subtract 30.39
from each side:                            0.12m  =  19.92

Divide each side by 0.12 :                  m  =  166 .

There it is !  If a car is rented from Gamma for a day, and another car
is rented from Delta for a day, and both cars are driven 166 miles, then
the rental prices for both cars will be the same ... (namely $121.69)