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In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an example of solving a system of linear equations. First, we present an example that we both use in our freshman algebra classes for modeling and problem solving and in our linear algebra class. Then we continue by giving a mathematical modeling algorithm for balancing the more complicated "oxidation-reduction" ("redox") equations using a system of linear equations.

Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem included higher order systems of differential equations in the solution. This paper discusses a new direction with modeling issues, several modeling based solutions, and numerical methods to solve these models using a spreadsheet. (Contains 2 figures and 3 tables.)