How many liters of a 40% sugar solution must be mixed with 30 liters of a 60% sugar solution to make a 56 % sugar solution?

Question

How many liters of a 40% sugar solution must be mixed with 30 liters of a 60% sugar solution to make a 56 % sugar solution?

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Alice 2 weeks 2021-09-09T13:19:23+00:00 1 Answer 0

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    2021-09-09T13:20:30+00:00

    Answer:

    7.5 liters

    Step-by-step explanation:

    Here what we need to know is the liters of the first solution, that we will call x. We know that the 40% of x plus the 60% of 30 MUST be equal to the 56% of total liters. The total liters are the sum of both substances, i.e, the x liters of the 1st sugar solution and the 30 liters of the second, which is 30+x liters. So, we have that:

    0.4*x + 0.6*30 = 0.56(30+x)

    Using distributive and the fact that 0.6*30 = 18 and 0.56*30=16.8

    0.4x + 18 = 16.8 + 0.56x

    Subtract 16.8 in both sides:

    0.4x + 18 – 16.8 = 0.56x

    0.4x + 1.2 = 0.56 x

    Subtract now 0.4x in both sides:

    1.2 = 0.56 x – 0.4x

    1.2 = 0.16x

    Divide both sides by 0.16

    1.2/0.16 = 0.16/0.16 x

    7.5 = x

    So, the first solution must be of 7.5 liters in order to have a 56% in the mixture.

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