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14 September, 03:53

Allison needs 18 liters of a 5% saline solution. She has a 1% solution and a 10% solution available. How many liters of the 1% solution and how many liters of the 10% solution should she mix to make the 5% solution?

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  1. 14 September, 06:43
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    10 liters of the 1% solution and 8 liters of the 10% solution she should mix to make the 5% solution.

    Explanation:

    Let the volume of 1% acid solution used to make the mixture = x L

    So, the volume of 10% acid solution used to make the mixture = y L

    Total volume of the mixture = x + y = 18 L ... (1)

    For 1% acid solution:

    C₁ = 1%, V₁ = x L

    For 10% acid solution:

    C₂ = 10%, V₂ = y L

    For the resultant solution of sulfuric acid:

    C₃ = 5%, V₃ = 18 L

    Using

    C₁V₁ + C₂V₂ = C₃V₃

    1*x + 10*y = 5*18

    So,

    x + 10y = 90 ... (2)

    Solving 1 and 2 we get,

    x = 10 L

    y = 8 L

    Thus,

    10 liters of the 1% solution and 8 liters of the 10% solution she should mix to make the 5% solution.
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