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)
