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27 July, 03:48

The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 120 pints of a mixture that is 65% pure fruit juice?

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  1. 27 July, 03:52
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    Make 2 equations from the question first

    x is the number of pints for type 1

    y is the number of pints for type 2

    The equation

    x + y = 120

    60% x + 85% y = 65% (x + y)

    Solve the equation

    From the 2nd equation

    0.6x + 0.85y = 0.65 (x + y)

    0.6x + 0.85y = 0.65x + 0.65y

    0.85y - 0.65y = 0.65x - 0.6x

    0.2y = 0.05x

    y = 4x

    From the 1st equation

    x + y = 120

    x + 4x = 120

    5x = 120

    x = 24

    y = 4x

    y = 96

    The first type should be 24 pints, the second type should be 96 pints
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