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28 December, 12:25

A box of nails weighs 130 pounds when it is 2/3 full. It weighs 74 pounds when it is 3/8 full. What is the weight of the box?

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  1. 28 December, 12:51
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    Let the weight of the full Volume of nails in the box be W.

    Let the weight of the box be B.

    2/3 W + B = 130 ... i From the first statement.

    3/8 W + B = 74 ... ii From the second statement.

    Equation (i) Minus (ii)

    2/3 W - 3/8 W + B - B = 130 - 74

    (16W - 9W) / 24 = 56

    7W / 24 = 56.

    W = 56 * 24 / 7

    W = 192 Pounds.

    Substituting V = 64 in equation (i)

    2/3 W + B = 130

    2/3 * 192 + B = 130

    2 * 64 + B = 130

    128 + B = 130

    B = 130 - 128 = 2.

    Therefore, weight of box, B = 2 pounds.
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