College Algebra

Question

A truck can be rented from Company A for $120 a day plus $0.40 per mile. Company B charges $80 a day plus $0.60 per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for Company A a better deal than Company B's?

Answer 1

Hello, thank you for taking the time to post your question!

I would start by setting the cost equations for each company equal to one another so that you can find the miles driven where it’s going to be the same charge for either one

120 + 0.4M = 80 + 0.6M

40 = 0.2M

M = 40/0.2 = 200

So at 200 miles the cost is equal, anything above that is going to make company A the better deal since they have the lower rate per mile … meaning that for the cost of Company A to be less than the cost of Company B the number of miles driven must be greater than 200

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

T = Total Cost

M = miles

 

Company A --> T = 120 + (0.4 * M)

Company B --> T = 80 + (0.6 * M)

 

 120 + (0.4 * M) = 80 + (0.6 * M)

 

40 + (0.4 *M) = (0.6 * M)

 

40 = (0.6 * M) - (0.4 * M)

 

40 = 0.6M - 0.4M

 

40 = 0.2M

 

M = 200

 

If you drive 200 miles the total cost for both company A and B are the same. Driving any more than 200 miles makes Company A a better deal.