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15 October, 15:53

Amy will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs an additional $0.80 per mile driven. The second plan has no initial fee but costs $0.90 per mile driven. How many miles would Amy need to drive for the two plans to cost the same?

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  1. 15 October, 18:15
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    Our two formulas for each plan:

    50 (base fee) +.80x (cost per mile) = y (total cost)

    .90x (cost per mile) = y (total cost)

    We want to find how many miles we have to drive, so solve for x. We're going to plug in y (from equation 2) into the value for y. This is the substitution method.

    50+.80x=y

    Plugin: 50+.80x =.90x

    Add. 90x to each side, subtract 50 from each side:.80x -.90x = - 50

    Simplify: -.10x = - 50

    Divide: x = - 50/-.10 (two negatives make a positive)

    x = 500

    So this tells us that she has to drive 500 miles to make the plans equal. Let's verify this by plugging in the value we found for x.

    @499 miles, plan 2 is cheaper.

    50 +.80 (499) = 449.20

    .90 (499) = 449.1

    @500 miles, they are equal

    50 +.80 (500) = 450

    .90 (500) = 450

    @501 miles, plan 1 is cheaper

    50 +.80 (501) = 450.8

    .90 (501) = 450.9

    We've verified our answer.
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