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19 September, 22:11

Lisa and Joey are each saving money for their prom. Lisa's total amount of money is represented by the function f (x) = 20-13x. The total amount of money Joey has is given by the function g (x) = x^2-10. After how many weeks, x, will they have the same amount of money saved? Show your work.

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  1. 20 September, 00:36
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    2 weeks

    Step-by-step explanation:

    Given in the question that,

    Equation that represent Lisa's total amount of money

    f (x) = 20 - 13x

    Equation that represent Joey's total amount of money

    g (x) = x² - 10

    To find weeks, x, after which they will have same amount of money, we will equate both equation

    20 - 13x = x² - 10

    x² - 10 - 20 + 13x = 0

    x² - 30 + 13x = 0

    x² + 13x - 30 = 0

    (x - 2) (x + 15) = 0

    x = 2 or x = - 15

    Weeks, x, can not be negative so we will reject x = - 15

    Hence, after 2nd week Lisa and Joey will have the same amount of money save.
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