Math Problem

[Jim Brier]

The problem with pluralizing students is that you give away the solution to the problem if you state: "the audience consists of adults, a student, and children." Perhaps I should have put on an additional constraint with something like: "(Note: There must be at least one adult)".

The reason this problem is an important one is that algebra students are conditioned to believe that when you have N unknowns, you must have N independent equations. But this is not true. You can solve a wide variety of important problems by having fewer equations than unknowns when you have constraints.

[BruceZ]

The reason this is solvable is because the solutions to the 2 equations in 3 unknowns must be positive integers. This is the additional constraint. Equations in more than one variable are called "diophantine equations" and are an important part of number theory.