A chemist needs to mix up 50 gallons of a 60% acid solution She only has 50% and 75% solutions on hand, How many gallons of each shoul

Question

A chemist needs to mix up 50 gallons of a 60% acid solution
She only has 50% and 75% solutions on hand, How many gallons of each should she mix together?

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Rylee 2 weeks 2021-09-10T08:13:28+00:00 1 Answer 0

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    2021-09-10T08:14:36+00:00

    x = gallons of the 50% solution

    y = gallons of the 75% solution

    The total volume of the new mixture is 50 gal, so

    x + y = 50

    Each gal of 50% solution contributes 0.5 gal of acid, and each gal of the 75% solution contributes 0.75 gal of acid. The final mixture needs to have a concentration of 60% acid, which amounts to 0.6*(50 gal) = 30 gal of acid, so

    0.5x + 0.75y = 30

    Solve for x and y :

    y = 50 – x

    0.5x + 0.75(50 – x) = 30

    0.5x + 37.5 – 0.75x = 30

    7.5 = 0.25x

    x = 30  ==>  y = 20

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