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4 November, 19:38

Suppose a lab needs to make 400 liters of a 39% acid solution, but the only solutions available to the lab are 20% acid and 50% acid. What system of equations can be used to find the number of liters of each solution that should be mixed to make the 39% solution? Let c represent the number of liters of 20% acid solution and let d represent the number of liters of 50% acid solution.

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  1. 4 November, 20:02
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    Mixture problem.

    Ratio of 20% : 50% acids

    =50-39 : 39-20

    =11:19

    total volume

    =400L

    vol. of 20% acid=400 * (11 / (11+19) = 400 * (11/30) = 146.667 L

    vol. of 50% acid=400 * (19 / (11+19) = 253.333 L

    Alternatively, use c=volume of 20%, d=vol of 50%

    then

    0.2c+0.5d=400*0.39

    Since c+d=400, we have

    0.2c+0.5 (400-c) = 400*0.39=156

    solve for c:

    0.3c=44

    c=146.667 and d=400-c=253.333 as before.
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