Question 1090516
<br>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.<br>
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.<br>
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<br>
{{{12 - 2.9 = (3/4)x - (1/6)x}}}
{{{9.1 = (9/12)x - (2/12)x}}}
{{{9.1 = (7/12)x}}}
{{{x = 9.1 * (12/7) = 15.6}}}<br>
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<br>
{{{12 = b+(3/4)(15.6)}}}
{{{12 = b+11.7}}}
{{{b = 0.3}}}<br>
The weight of the box is 0.3 pounds.