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Math Help - Systems of Eqns. Word Problem

  1. #1
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    Systems of Eqns. Word Problem

    Write a system of equations in x and y and solve.

    How much of a 40% antifreeze solution must a mechanic mix with 7% antifreeze solution to have 20 gallons of a 50% anti freeze solution?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by HSS8 View Post
    Write a system of equations in x and y and solve.

    How much of a 40% antifreeze solution must a mechanic mix with 7% antifreeze solution to have 20 gallons of a 50% anti freeze solution?
    (x of 40%) +(y of 7%) = 20 of 50%
    40x +7y = 1000 -----------------------(1)

    x +y = 20 -----------(2)

    Can you solve that now?

    You should get
    x = 26.06 gal
    y = -6.o6 gal

    Hey, wait a minute. A negative volume for the 7% antifreeze?
    Cannot be.

    Umm, the mechanic is trying to get a mixture of 50% from mixing some 40% and some 7%? Cannot be. 50% is both higher than each of the 40% and 7%.
    One of the components must be higher than 50%.

    So, I think the 7% should be 70%. A typo in your question.

    Then
    40x +70y = 1000
    4x +7y = 100 -----------(1a)

    x +y = 20 -------------still (2)

    You should get now:
    x = 13 and 1/3 gallons
    y = 6 and 2/3 gallons
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