SOLUTION: a box of sand weighs 12 lbs when it's 3/4 full. It weighs 2.9 lbs when it's 1/6 full. What is the weight of the box?

Question 1090516: a box of sand weighs 12 lbs when it's 3/4 full. It weighs 2.9 lbs when it's 1/6 full. What is the weight of the box?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Let box=weight of box itself
box +(3/4) sand=12 the weight of the box + 3/4 of it full of sand is 12 pounds
box +(1/6) sand=2.9; same approach
box=12-(3/4)sand
box=2.9-(1/6)sand. Here solving each of the above for box. I now have box = to two different things. Therefore, those two different things are equal to each other.
Therefore 12-(3/4) S=2.9-(1/6)S
9.1=(7/12)S
S=15.6 pounds if full.
But Box and 3/4 S is 12 pounds.
The sand for (3/4) weighs 11.7 pounds, and the box weighs 0.3 pounds
The sand for (1/6) weighs 2.6 pounds, and the box weighs 0.3 pounds
ANSWER
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

My solution will algebraically end up looking almost exactly the same as the solution provided by Boreal. But I use a different thought process to get started on solving the problem, so in the beginning my work looks different.

My thought in getting started is that the 12 pounds and 2.9 pounds both include the weight of the box, so the difference between the 12 pounds and the 2.9 pounds will be because of the different amounts of sand.

The 12 pounds is the weight of the box plus 3/4 of the sand needed to fill the box; the 2.9 pounds is the weight of the box plus 1/6 of the sand needed to fill the box. So if we let x be the weight of the sand needed to fill the box, we have

Again, the 12 pounds is the weight of the box plus the weight of 3/4 of the sand needed to fill the box. If we call the weight of the box b, then

The weight of the box is 0.3 pounds.
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