Question

Jodi is cutting out pieces of paper that measure 8 1/2 inches by 11 inches from a larger sheet of paper that has an area of 1,000 square inches. What is
the greatest possible number of pieces that Jodi can cut out of the larger sheet?

Answer 1

All you know is that the area of this large piece of paper is 1000 square inches; you don't know the length or width. If the length is represented by L and the width by W, then the area is L*W=1000. That's your "constraint."

You are to cut out pieces of paper that are 8 1/2 inches by 11 inches. The area of such a piece would be (8 1/2 inches)(11 inches) = 93 1/2 square inches. What might you do with this information? Note that if you divide that 93 1/2 square inches into that 1000 square inches, you may find that there is a remainder. That's life!

Why not sketch this situation, showing how you might fit ten or so pieces of paper 8 1/2 inches by 11 inches into your 1000 square inch area. Play around with this layout. What appears to be the max number of pieces of paper 8 1/2 inches by 11 inches that you can fit into 1000 square inches? Note that this would minimize the wasted paper from the 1000 square inch piece.