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22 September, 16:45

One antifreeze solution is 31% alcohol and another is 15% alcohol. How much of each mixture should be added to make 28 L a solution that is 27% alcohol?

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  1. 22 September, 16:46
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    Let

    x = volume of the 31% solution

    y = volume of the 15% solution

    We want a solution with a total volume of 28 L, so

    x + y = 28

    For each liter of either solution, there is a contribution of 0.31 L and 0.15 L of alcohol, respectively. In the resulting solution, we want a concentration of 27% alcohol, which comes out to 0.27 * 28 L = 7.56 L. So

    0.31 x + 0.15 y = 7.56

    The first equation says

    y = 28 - x

    Substitute this into the second equation and solve for x, then for y:

    0.31 x + 0.15 (28 - x) = 7.56

    0.31 x + 4.2 - 0.15 x = 7.56

    0.16 x = 3.36

    x = 21

    y = 28 - x

    y = 7
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