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13 December, 07:06

A scientist wants a 66 ounce saline solution with concentration 12%. She has concentrations of 4% and 15%. How much of each solution must she use to get the desired concentration?

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  1. 13 December, 07:20
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    Let x and y represent the measure in ounces of the two given saline solutions. We are mixing these two together, so x + y = 66 ounces.

    The amount of the 4% solution to be used is 0.04x, and that of the 15% solution is 0.15y.

    This results in the equation. 04x + 0.15y = 66 (0.12).

    Multiply both sides by 100 to remove the decimal fractions. Then

    4x + 15y = 66 (12). Now eliminate the variable x by recalling that x + y = 66 ounces, so that x = 66 - y.

    Substituting, 4 (66 - y) + 15y = 66 (12)

    Expanding, 264 - 4y + 15 y = 792

    combining like terms: 11y = 528

    Solving for y: y = 528/11 = 48. Then x = 66 - 48 = 18.

    Use 48 ounces of the 15% solution and 18 ounces of the 4% solution to obtain 66 ounces of a 12% solution.
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