Question

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?

Answer 1

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.