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12 January, 04:01

How many gallons of a 30% salt solution must be added to 40 gallons of a 12% salt solution to obtain a 20% solution?

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  1. 12 January, 04:20
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    Let’s call the number of gallons of 30% solution "x". If we mix together 40 gallons and x gallons of solution, we’re going to come out with a total of 40 + x gallons of that 20% solution. Mathematically, this is

    40 (12%) + x (30%) = (40 + x) (20%)

    With the percents as decimals:

    40 (0.12) + x (0.3) = (40 + x) (0.2)

    Simplifying, we have:

    4.8 + 0.3x = 8 + 0.2x

    Collecting the x terms on one side and the constants on the other:

    0.1x = 3.2

    And multiplying both sides by 10 to find x:

    x = 32

    So, you’ll need 32 gallons of 30% solution to yield 40 + 32 = 72 gallons of 20% solution.
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