the following problem appears as a "brainteaser" in the fifth edition of Mathematics for Elementary School Teachers by Billstein, Libeskind, and Lott (1993, 298). It is an excellent problem for students, since it can be solved nicely either by using a straightforward algebraic approach or by working backward. In producing what was thought to be an equivalent form for an examination question, the authors accidentally afforded students an excellent opportunity to discuss the age-old question of "What if…?