Question

A truck can be rented from company A for $90 a day plus $0.20 per mile. Company B charges $60 a day plus $0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for company A and company B are the same.

a) 100 miles

b) 120 miles

c) 80 miles

d) 150 miles

Answer 1

The rental costs for company A and company B are the same at 100 miles driven. This is found by setting up an equation with the cost formulas from both companies and solving for the number of miles.

Step-by-step explanation:

To find the number of miles at which the rental costs for company A and company B are the same, we can set up an equation where the total cost of renting the truck from each company is equal. Let the variable m represent the number of miles driven.

Company A charges $90 per day plus $0.20 per mile, so their cost is represented as 90 + 0.20m. Company B charges $60 per day plus $0.50 per mile, represented as 60 + 0.50m.

Equating the two costs and solving for m:

90 + 0.20m = 60 + 0.50m

Moving the variables on one side and constants on the other:

0.30m = 30

Divide both sides by 0.30 to find m:

m = 30 / 0.30

m = 100 miles

The rental costs for company A and company B are the same at 100 miles.