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Math Help - Mixture story problem

  1. #1
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    Mixture story problem

    Trying to learn how to do these types of problems. The last one I had for homework was wrong.

    How much 12% Na2SO4 and pure water must be mixed to produce 22.8 gallons of a mixture that is 7% sodium sulfate?

    I started with: Let x = the # of gallons of 12% Na2SO4
    And Let y = the # of gallons of 100% water

    Now I thought I do (value)(quantity).

    I plugged:
    (0.12)(x)+ (0.100)(w) = (0.07)(22.8)

    and then I distributed -

    0.12x+0.100w=1.596

    Now I am not sure if that is correct. And if it is, I am stuck on what to do next?
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  2. #2
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    Re: Mixture story problem

    Quote Originally Posted by Kibbygirl View Post
    Trying to learn how to do these types of problems. The last one I had for homework was wrong.

    How much 12% Na2SO4 and pure water must be mixed to produce 22.8 gallons of a mixture that is 7% sodium sulfate?

    I started with: Let x = the # of gallons of 12% Na2SO4
    And Let y = the # of gallons of 100% water

    ...
    1. Using your labeling you already know:

    \left|\begin{array}{rcl}x+y&=&22.8 \\ 0.12x&=& 0.07(x+y) \end{array} \right.

    2. Solve for x and y. I've got (x,y) = (13.3, 9.5)
    Thanks from Kibbygirl
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  3. #3
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    Re: Mixture story problem

    Code:
    a   @ x
    b   @ y
    ========
    a+b @ z
    
    z = (ax + by) /(a+b)
    
    a      @ 12
    22.8-a @  0
    ===========
    22.8   @  5
    
    5 = (12a + 0) / 22.8
    a = 13.3
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