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19 October, 12:05

Myra is a scientist and needs 45 gallons of a 16% acid solution. The lab is currently stocked only with a 20% acid solution and a 10% acid solution. Myra will need to mix how many gallons of the 20% solution and how many gallons of the 10% solution to have what she needs.

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  1. 19 October, 14:13
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    The volume of the solution with 20% acid is 27 gallons and the one with 10% acid is 18 gallons

    Step-by-step explanation:

    Myra needs to mix "x" gallons of the solution with 20% and "y" gallons of the solution with 10%. The volume of the final solution must be 45 gallons, therefore:

    x + y = 45

    The concentration of acid of the final solution is:

    0.2*x + 0.1*y = 45*0.16

    0.2*x + 0.1*y = 7.2

    Therefore we have a system of equation:

    x + y = 45

    0.2*x + 0.1*y = 7.2

    We need to multiply the first equation by - 0.1:

    -0.1*x - 0.1*y = - 4.5

    0.2*x + 0.1*y = 7.2

    We now sum both equation:

    0.1*x = 2.7

    x = 2.7/0.1 = 27 gallons

    y = 45 - 27 = 18 gallons
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