Question

Rent-Me Rent-A-Car charges $25.00 per day plus $0.14 per mile to rent an economy car. Better Deal Rental Car charges $23.00 per day plus $0.18 per mile for the same type of car. For how many miles will a car rented from either company cost the same amount?

Answers

  1. Answer:

    The number of miles at which a car rented from either company cost the same amount is 50 miles.

    Step-by-step explanation:

    Let x represents the number of miles at which a car rented from either company cost the same amount. Therefore, we can have the following equation:

    RC = 25 + 0.14x ………………….. (1)

    BC = 23 + 0.18x …………………. (2)

    Where;

    RC = Total cost of Rent-Me Rent-A-Car

    BC = Total cost of Better Deal Rental Car

    The the cost of the two companies equal where RC = BC. Therefore, we equate equations (1) and (2) and solve for x as follows:

    25 + 0.14x = 23 + 0.18x

    25 – 23 = 0.18x – 0.14x

    2 = 0.04x

    x = 2 / 0.04

    x = 50

    Therefore, the number of miles at which a car rented from either company cost the same amount is 50 miles.

    Note:

    This can be confirmed for equations (1) and (2) individually by substituting for x = 50 as follows:

    For equation (1):

    RC = 25 + 0.14(50)

    RC = 25 + 7

    RC = 32

    For equation (2):

    BC = 23 + 0.18(50)

    BC = 23 + 9

    BC = 32

    Therefore, RC = BC = 32 confirms the answer.

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