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Math Help - Algebra word problem

  1. #1
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    Algebra word problem

    I have a word problem that I know the answer is supposed to be 5 liters, however, that is not the answer I'm getting when I solve it. Can anyone help?

    Word problem: It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now holds 20 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength? (Hint: the number of liters drained is equal to the number of liters replaced.)

    This is the formula I am using, of course, maybe this is my problem.

    .20 (20) - .20x + 1.0 (x) = .40 (20)

    Please help!
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  2. #2
    MHF Contributor
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    Apr 2008
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    The key is that the total amount of liquid is still going to be equal to 20 liters in the end, so the final 40% solution will contain 8 liters of antifreeze.

    Let's say that x is the amount of 100% solution you replace the 20% solution with.

    So you want .2(20 - x) + x = 8. Just solve for x. Edit: this is the same as you came up with, and the answer is indeed 5. Perhaps your calculations went awry?
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