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Math Help - Mixture Problem

  1. #1
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    Mixture Problem

    I encountered the following problem:

    10 grams of water is added to a 30% solution of barium chloride to dilute the solution to 20%. How many grams of the original solution did we start with?

    The answer is 20 grams calculated as follows:

    Let x = the number of grams of the original solution.

    (0.20)(10+x) = 0.30x
    x = 20

    I then asked myself this question: How would the solution to this problem be changed if, instead of adding 10 grams of water to dilute the solution to 20%, 10 grams of barium chloride were added to strengthen the solution to 40%?

    It seems to me that the only thing that would change would be that 0.20 would be changed to 0.40. That results in a negative value for x. What am I missing?

    Thanks for any input.

    ... doug
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  2. #2
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    Re: Mixture Problem

    Quote Originally Posted by ddjolley View Post
    I encountered the following problem:

    10 grams of water is added to a 30% solution of barium chloride to dilute the solution to 20%. How many grams of the original solution did we start with?

    The answer is 20 grams calculated as follows:

    Let x = the number of grams of the original solution.

    (0.20)(10+x) = 0.30x
    x = 20

    I then asked myself this question: How would the solution to this problem be changed if, instead of adding 10 grams of water to dilute the solution to 20%, 10 grams of barium chloride were added to strengthen the solution to 40%?

    It seems to me that the only thing that would change would be that 0.20 would be changed to 0.40. That results in a negative value for x. What am I missing?

    Thanks for any input.

    ... doug
    when you add water, it is a 0% concentration of the substance

    10(0%) + x(30%) = (10 + x)(20%)

    30x = 200 + 20x

    x = 20 g

    when you add 10 g of pure substance ...

    10(100%) + x(30%) = (10 + x)(40%)

    1000 + 30x = 400 + 40x

    600 = 10x

    x = 60 g
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  3. #3
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    Nov 2011
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    Re: Mixture Problem

    Ah!!! I knew that it was something stupid like that! Thanks so much.

    ... doug
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