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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

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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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