Equations with variables on both sides

Discussion in 'Algebra' started by austindee, Jan 31, 2019.

  1. austindee

    austindee

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    I am looking for the equation for this problem. I know the answer is 105 minutes. I see the answer as a ratio, but I need to set up an equation for the solution.

    Selma's class is making care packages to give to victims of a natural disaster. Selma packs one box in 5 minutes and has already boxed 12 boxes. Her friend Trudy packs one box in 7 minutes and has already boxed 18 boxes. How many more minutes does each need to work in order to have packed the same number of boxes?
     
    austindee, Jan 31, 2019
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  2. austindee

    alan whittle

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    The key to this is to determine the number of boxes they will both have made. Call this N, so that Selma must make N - 12 more and Trudy N - 18.
    This will take 5(N -12) minutes for Selma and 7(N-18) for Trudy.
    You find N from the fact that these are equal.
    Hence N = 33, and so Selma needs 21 more and Trudy 15.
    As you say, this takes each of them 105 minutes
     
    alan whittle, Dec 17, 2019
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