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)
