Jasmine is a manufacturing engineer who is trying to find out if she can use a 20-inch-by-12 inch sheet of cardboard and a 15-inch-by-16-inch sheet of cardboard to make boxes with the same height and volume. Is such a pair of boxes possible?
Please give mathematical proof.
The problem is not clearly enough defined. Certainly you could make a pair of small boxes of equal volume and height, with material left over from both pieces.
Conider a pair of 4 x 4 x 4 inch boxes, for example. All you need is a 12 x 12 x 12 sheet.