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1 December, 19:39

Sue plans to mix peppermints worth $1.20 per lb with chocolates worth $2.40 per lb to get a 40 lb mix that is worth $1.65 per lb. How much of each should she use?

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  1. 1 December, 19:56
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    Each should be used as follows:

    Weight of peppermints = X = 25 lb

    Weight of Chocolates = Y = 15 lb

    Explanation:

    Suppose

    Weight of peppermints = X

    Weight of Chocolates = Y

    So According to given condition

    X + Y = 40 (Eq. 1)

    1.2X + 2.4Y = 1.65*40

    1.2X + 2.4Y = 66 (Eq. 2)

    By multiplying (Eq. 1) with 1.2 we get

    1.2X + 1.2Y = 48 (Eq. 3)

    Now by subtracting (Eq. 2) from (Eq. 3)

    (1.2X + 1.2Y) - (1.2X + 2.4Y) = 48 - 66

    1.2X + 1.2Y - 1.2X - 2.4Y = - 18

    1.2X - 1.2X + 1.2Y - 2.4Y = - 18 (Rearrange)

    -1.2Y = - 18

    1.2Y = 18

    Y = 18/1.2

    Y = 15

    By placing value of Y in (Eq. 1)

    X + 15 = 40

    X = 40 - 15

    X = 25

    Check

    1.2X + 2.4Y = 66

    1.2 (25) + 2.4 (15) = 66

    66 = 66
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