Final answer:
Using the given pricing structures for Primo and Ultimo car rental agencies, we set up an equation based on the condition that Ultimo's charge is four times Primo's charge. After simplifying the equation, we find that at 2300 miles, Ultimo's charge will be four times that of Primo's.
Step-by-step explanation:
To find the daily mileage for which the Ultimo charge is four times the Primo charge, we first set up an equation using the pricing structures given for both rental agencies. Primo's charge is $33 per day plus $0.20 per mile, and Ultimo's charge is $17 per day plus $0.85 per mile.
The formula for Primo's charge (P) based on the number of miles (m) driven is:
P = 33 + 0.20m
Similarly, for Ultimo's charge (U):
U = 17 + 0.85m
The condition given is that Ultimo's charge is four times Primo's charge, which leads us to the equation:
4(P) = U
Substituting the expressions for P and U, we get:
4(33 + 0.20m) = 17 + 0.85m
This simplifies to:
132 + 0.80m = 17 + 0.85m
By subtracting 0.80m from both sides, we isolate the variable:
132 = 17 + 0.05m
After subtracting 17 from both sides, we get:
115 = 0.05m
Now, dividing both sides by 0.05, we find the number of miles (m):
m = 2300
This means that at 2300 miles, Ultimo's charge will be four times Primo's charge.