# Car Rental Math Problem

Car Rental Math Problem

Evaluating Choices:

A major car rental firm “A” charges RM60 a day with no additional charges for mileage. However, a discount firm “B” offers a similar car for RM 24 per day plus 30 cents per mile. For a certain traveling distance, is it better to rent a car from A or B?

### Comments for Car Rental Math Problem

 Aug 26, 2012 Evaluating Rental Choices by: Staff Answer: Cost of Any Car Rental Cost = (Cost per Day)*(Number of Days) + (Cost per Mile)*(Number of Miles Driven) Cost of Renting from Firm “A” Cost of renting from Firm “A” = A Cost per Day = RM60 Number of Days = D Cost per Mile = 0 Number of Miles Driven = N Cost = (Cost per Day)*(Number of Days) + (Cost per Mile)*(Number of Miles Driven) A = 60*D + 0*N A = 60*D + 0 A = 60*D A = 60*D Cost of Renting from Firm “B” Cost of renting from Firm “B” = B Cost per Day = RM24 Number of Days = D Cost per Mile = 30 cents Number of Miles Driven = N Cost = (Cost per Day)*(Number of Days) + (Cost per Mile)*(Number of Miles Driven) B = 24*D + 0.30*N B = 24D + .3N The two equations which will be used for comparison are: A = 60*D B = 24D + .3N Subtract the second equation from the first equation (this will be the cost difference between renting from Firm “A” or Firm “B”) A - B = 60*D - (24D + .3N) A - B = 60*D - 24D - .3N A - B = 36D - .3N If there is no cost difference (break even point) Solve for N 0 = 36D - .3N Add .3N to each side of the equation 0 + .3N = 36D - .3N + .3N 0 + .3N = 36D + 0 .3N = 36D Divide each side of the equation by .3 .3N / .3 = 36D / .3 N * (.3 / .3) = 36D / .3 N * 1 = 36D / .3 N = 36D / .3 N = D * (36 / .3) N = D * 120 N = 120D For one day (D = 1): N = 120*1 N = 120 miles The number of miles which can be driven per day so that the costs of A and B are equal = 120 miles. Final Answer    • If you drive less than an average of 120 miles per day, the cost of renting from Firm “B” is less expensive than Firm “A”.    • If you drive more than an average of 120 miles per day, the cost of renting from Firm “A” is less expensive than Firm “B”. Thanks for writing. Staff www.solving-math-problems.com

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