Question

Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use.

How much of the 10% alcohol solution should Bruce use?

mL

How much of the 15% alcohol solution should Bruce use?

mL

Answers

  1. The amount of the 10% alcohol solution  that Bruce should use is 30ml and the amount of the 15% alcohol solution  that Bruce should use is 20ml.

    Alcohol solution

    Given:
    Equation 0.10x + 0.15(50 – x) = 0.12(50)
    Let x represent  10% alcohol solution that Bruce should use
    Hence:
    0.10x + 0.15(50 – x) = 0.12(50)
    0.10x + 7.5-0.15x=6
    Collect like term
    0.10x-0.15x=6-7.5
    -0.05x=-1.5
    Divide both side by -0.05x
    x=-1.5/-0.05
    x=30 ml
    b. 15% alcohol solution
    (50 – x), when x=30 ml
    (50-30)
    =20 ml
    Therefore the amount of the 10% alcohol solution  that Bruce should use is 30ml and the amount of the 15% alcohol solution  that Bruce should use is 20ml.
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