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25 March, 07:40

Keisha will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0.15 per mile driven. The second plan has an initial fee of $53 and costs an additional $0.13 per mile driven.

For what amount of driving do the two plans cost the same?

What is the cost when the two plans cost the same?

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  1. 25 March, 07:43
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    650 miles has to driven before the plans cost the same

    When the two plans cost the same, the cost is $ 137.5

    Solution:

    Given that, Keisha can choose one of two plans

    Let "n" be the number of miles driven

    For Keisha 1st Plan:

    The first plan has an initial fee of $40 and costs an additional $0.15 per mile driven

    Therefore,

    Cost of plan 1 = 40 + (0.15) n

    For Keisha 2nd plan:

    The second plan has an initial fee of $53 and costs an additional $0.13 per mile driven

    Cost of plan 2 = 53 + (0.13) n

    To find out the number of miles where the two plans cost the same set the two expressions equal to each other and solve for n

    40 + 0.15n = 53 + 0.13n

    0.15n - 0.13n = 53 - 40

    0.02n = 13

    n = 650

    Thus 650 miles has to driven before the plans cost the same

    Substitute 650 in any one of equations

    40 + 0.15n = 40 + (0.15) (650) = 40 + 97.5 = 137.5

    When the two plans cost the same, the cost is $ 137.5
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