Question

A truck can be rented from Company A for ​$100 a day plus ​$0.40 per mile. Company B charges ​$40 a day plus ​$0.80 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.

Answer 1

150 miles

Explanation:

Let x be the number of miles driven/

Company A: $100/day + ($0.40/mile)*x = Total A

Company B: $40/day + ($0.80/mile)*x = = Total B

At what x (number of days) are the amounts equal:

$100/day + ($0.40/mile)*x = $40/day + ($0.80/mile)*x

($60/day) = ($0.40/mile)*x

For a 1 day rental:

(1 day)*($60/day) = ($0.40/mile)*x

($0.40/mile)*x = $60

x = ($60)/($0.40/mile)

x = 150 miles

Check:

Company A: $100/day + ($0.40/mile)*(150 miles) = Total A

Company B: $40/day + ($0.80/mile)*(150 miles) = Total B

Company A: $100/day + $60 = Total A = $160

Company B: $40/day + ($120) = Total B = $160 Checks OK