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15 March, 06:25

pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10 liters of a 20% alcohol solution?

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  1. 15 March, 06:47
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    9.09 Liters of 18% solution

    .91 Liters of 40% Solution

    Step-by-step explanation:

    You have to solve a system of equations for this problem. But first, let's figure out what we know.

    We know we end up with 10L of total solution, at 20% concentration.

    So, we know we have 10 * 0.2 = 2L of total alcohol in the solution.

    Consider the 18% solution "x" and the 40% solution "y." Express the percentages as decimals, so. 18 and. 4 respectively. Putting this all together,

    we create the first equation:

    .18x +.4y = 2

    We also know that the amount of 18% solution, or x, combined with the 40% solution, y, must equal 10L. So our second equation is

    x + y = 10

    We'll solve the second one first, for x. Rearranging the equation gives you

    x = 10 - y

    Now, put this value for x into the first equation, in place of the current x term. Doing so gives you

    .18 (10-y) +.4y = 2

    Distributing the ".18" gives you

    1.8 -.18y +.4y = 2, which is the same as

    0.22y = 0.2 when you combine the like terms.

    This means, y =.2/.22 = 0.91L of 40% solution

    Inserting our new y-value into the second equation gives us

    x + 0.91 = 10, or x = 10 - 0.91 = 9.09L of 18% solution
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