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Math Help - word problem;

  1. #1
    Newbie annabananzaa's Avatar
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    word problem;

    how many liters of a 25%alcohol solution must be mixed with a 12% solution to get 13 liters of a 15% solution.

    i have always had trouble interpreting math problems. once i get pushed in the right direction, im pretty sure i will be able to solve the equation.
    pleasee and thank youu!
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  2. #2
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    Hello, annabananzaa!

    How many liters of a 25% alcohol solution must be mixed with a 12% solution
    to get 13 liters of a 15% solution.?
    These "mixture problems" can be solved if we organize our facts.


    Let x = liters of 25% solution.
    Then 13-x = liters of 12% solution.
    (I hope you see why.)


    The x liters of 25% solution contains: . 0.25x liters of alcohol.

    The 13-x liters of 12% solutions contains: . 0.12(13-x) liters of alcohol.

    . . Hence, the mixture will contain: . 0.25x + 0.12(13-x) liters of alcohol. .[1]


    But we know that the final mixture will be 13 liters which is 15% alcohol.
    . . It will contain: . 0.15(13) \:=\:1.95 liters of alcohol. .[2]


    We just described the final amount of alcohol in two ways.
    There is our equation! . . . Equate [1] and [2]

    . . . . 0.25x + 0.12(13-x) \;=\;1.95


    Got it?

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  3. #3
    Newbie annabananzaa's Avatar
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    yess! i get it!

    its always the wording and translation into a equation that i have problems with.

    thank you so much for taking out the time to explain it to me!
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