Chapter 5.2, Problem 48MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinctly, and of uncovering pattern and structure.

Möbius prep (H). You have a large rectangular sheet of paper, x inches by y inches, with y measuring the longer side. You want to cut this sheet into rectangular strips, $\mathrm{½}$ in by 6 inches, for making Möhius hands. You know that y is a multiple of 6 and $x$ is a natural numhcr. What values of $x$ and y will allow you to create exactly 72 bands? (hint Feel free to use guess-and-check to determine your answer.)