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26 February, 07:13

he first solution contains 25 % acid, the second contains 35 % acid, and the third contains 55 % acid. She created 100 liters of a 45 % acid mixture, using all three solutions. The number of liters of 55 % solution used is 3 times the number of liters of 35 % solution used. How many liters of each solution was used?

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  1. 26 February, 10:42
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    Volume of first solution = 20 Liters

    Volume of second solution = 20 Liters

    Volume of third solution = 60 Liters

    Explanation:

    Let the volume second solution used = y

    Let the volume of third solution used = 3y

    Let the volume of first solution used = 100 - (y + 3y)

    = 100 - 4y

    The volume of acid in the first solution (V₁) = 25% of (100-4y)

    = 25-y

    The volume of acid in the second solution (V₂) = 35% of y

    = 0.35y

    The volume acid in the third solution (V₃) = 55% of 3y

    =1.65y

    The Volume of acid in Mixture (V₄) = 45% of 100

    = 45

    From the conservation of volume:

    V₄ = V₁ + V₂ + V₃

    45 = (25-y) + 0.35y + 1.65y

    45 = 25 - y + 0.35y + 1.65y

    45 - 25 = y

    y = 20

    So the volume of first solution used = 100 - 4y

    = 100 - 4 (20)

    = 20 Liters

    So the volume of second solution used = y

    = 20 Liters

    So the volume of third solution used = 3y

    = 3 (20)

    = 60 Liters
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