Question 1112659
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You can solve the problem algebraically and/or intuitively.


Intuitive solution is this:


<pre>
    On each gallon of the 10% solution take 3 gallons of the 30% solution.


    It works, since  {{{(0.1*1 + 0.3*3)/(3 + 1)}}} = {{{1.0/4}}} = 0.25 = 25%.


    Thus you get 5 groups/packages each containing (1 gallon of the 10% solution PLUS 3 gallons of the 30% solutions),

    which gives you 5 gallons of the 10% solution AND 15 gallons of the 30% solutions, in all.
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Algebraic solution is this:


<pre>
    {{{(0.1*x + 0.3*(20-x))/20}}} = 0.25.


    saying that the concentration of the mixture is 25% = 0.25.


    The steps to solve it are

        0.1x +0.3*(20-x) = 0.25*20

        0.1x + 6 - 0.3x = 5

        -0.2x = 4 - 5 = -1  ====>  x = {{{(-1)/(-0.2)}}} = 5.


    You get the same answer:  5 gallons of the 10% solution and (20-5) = 15 gallons of the 30% solution.
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Solved.