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Math Help - Mixing ingredients where portion of one of ingredients is a fn of the final amount

  1. #1
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    Mixing ingredients where portion of one of ingredients is a fn of the final amount

    I have two mixtures of flour and water.

    Mixture 1 has equal parts flour and water

    Mixture 2 has two parts flour to one part water

    I also have supplies of flour and water

    Problem (a) I'm going to mix flour and water and want to end up with mixture 1 -- equal parts flour and water. BUT in doing so I have to include an amount of Mixture 2 that is 1/6 of the total amount of mixture I end up with (i.e., 1/6 of the total of flour, water, and mixture 2).

    Problem (b) is similar -- I'm going to mix flour and water and want to end up with mixture 2 -- two to one ratio of flour to water. BUT I have to include an amount of Mixture 1 that is 1/7 of the total end result.



    This is my first post and not a school/college question


    At 58 am a bit rusty on this stuff hence the question here.


    My initial thoughts


    F= flour
    W= water
    M1 = Mixture 1 = 0.5F +0.5W
    M2 = Mixture 2 = 2.0F +1.0W


    Ma = Mixture a = 0.5F + 0.5W at the end but must be made up of enough of M2 so as to constitute 1/6th of Ma



    Ma = xF + yW + 1/6 (Ma)(M2).....
    Thanks
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  2. #2
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    The equation you wrote looks sensible, but you need more than 1 equation to solve the problem.

    If you define:

    F = the amount of flour you added
    W = the amount of water you added
    M2 = the amount of mixture 2 added

    The total amount of water in your output is
    \frac{1}{3}M2 + W

    And the total amount of Flour is
    \frac{2}{3}M2 + F

    To end up with mixture1, you need to have the same amount of flour and water
    \frac{2}{3}M2 + F = \frac{1}{3}M2 + W

    You are also told to use M2 for 1/6 of your input, which means there should be 5 units of standalone (flour + water) for each 1 units of M2.
    (F + W) = 5M2

    Now all you need to do is decide how much mixture to make, to do this set an arbitrary amount of one of the ingredients eg
    M2 = 1

    Then solve the other two equations simultaneously.
    \frac{2}{3} + F = \frac{1}{3} + W
    (F + W) = 5


    Which has a solution of
    W=7/3
    F = 8/3
    M2 = 1

    NB post was edited to fix a mistake earlier
    Last edited by SpringFan25; April 12th 2011 at 06:31 AM. Reason: corrected mistake..again
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