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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05-01-2015
Mathematics

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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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olemakpadu olemakpadu · Answer 1 · 2015-01-05T09:42:17-05:00

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.