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Math Help - percent equation

  1. #1
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    percent equation

    Hi, everyone! I am so happy to find this friendly and supportive forum , glad to be part of it. I just started taking classes in college this fall, and math is one of the subject I have to work hard. I am doing OK so far but there are problems I am finding hard to solve. One of them is a word problem using the percentage. I had spent almost all day today, trying to solve it and finally I am giving up and asking for help. I will appreciate the help. A hospital needs to dilute a 60% boric acid solution to a 10% solution. If it needs 40 liters of the 10% solution, how much of the 60% solution and how much water should it use?
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  2. #2
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    Hello, mirdita59!

    Welcome aboard!


    A hospital needs to dilute a 60% boric acid solution to a 10% solution.
    If it needs 40 liters of the 10% solution, how much of the 60% solution
    and how much water should it use?

    Let x = amount of 60% solutions to be used.
    Then 40-x = amount of water to be used.

    Consider the amount of boric acid in each stage.

    We used x liters of the 60% solution.
    . . This contains: 0.6x liters of boric acid.

    We add 40-x liters of pure water.
    . . This contains: 0 liters of boric acid.

    The mixture contains: . 0.6x + 0 \:=\:0.6x liters of boric acid.


    But we are told that the final 40 liters should be 10% boric acid.
    . . Hence, it will contain: . (40)(0.10) \:=\:4 liters of boric acid.

    There is our equation: . 0.6x \:=\:4\quad\Rightarrow\quad x \,=\,\frac{20}{3}

    Therefore, we should use 6\frac{2}{3} liters of the 60% solution and 33\frac{1}{3} liters of water.

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  3. #3
    MHF Contributor
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    A hospital needs to dilute a 60% boric acid solution to a 10% solution. If it needs 40 liters of the 10% solution, how much of the 60% solution and how much water should it use?

    Water is 0% acid.

    So final volume of liquid is 40 liters.

    Let x = volume of 60% acid solution to be mixed, in liters.
    So, (40-x) liters of water is to be added.

    x(60%) +(40-x)(0%) = 40(10%)
    Divide both sides by 1%,
    x(60) +0 = 40(10)
    x = 400/60 = 6.667liters, or (6 and 2/3) liters

    Therefore,
    6 and 2/3 liters of 60% boric acid solution
    and (40 -6.667) = 33.333 liters, or 33 and 1/3 liters of water
    should be used. --------------answer.
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