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

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)