Can you follow this solution to a recreational math problem?

I have a Web page for high school level math. Part of the site is a collection of recreational problems. I recently came across a problem in a book that I would like to include. I give due credit to the author for the problem and give my technique for solving it, which is different from that given in the book. The solution mostly requires knowledge of nothing more than basic arithmetic, but I am afraid that it might still be difficult to follow. If you have a few minutes to spare, I would appreciate your feedback before I decide whether to use the problem. The problem