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25 August, 21:01

Shaun needs to produce 1000 milliliters of 36% alcohol solution. At his disposal he has 20% alcohol solution and 40% alcohol solution. How much of each does he need in order to produce his desired solution?

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  1. 25 August, 21:29
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    The answer to your question is 200 ml of the solution 20% and 800 ml of the solution 40%.

    Explanation:

    Data

    Total volume = V = 1000 ml

    Final concentration = F = 36%

    Concentration of solution 1 = c1 = 20%

    Concentration of solution 2 = c2 = 40%

    Volume of solution 1 = v1 = ?

    Volume of solution 2 = v2 = ?

    Process

    1. - Write an equation to solve this problem

    FV = c1v1 + c2v2

    2. - Write volume in terms of total volume

    Total volume = V

    v1 = x

    v2 = 1000 - x

    3. - Substitution

    (36) (1000) = 20x + 40 (1000 - x)

    Solve for x

    36000 = 20x + 40000 - 40x

    36000 - 40000 = 20x - 40x

    -4000 = - 20x

    x = - 4000/-20

    x = 200

    Then v1 = 200 ml

    and v2 = 1000 - v1

    = 1000 - 200

    = 800 ml
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