## An example of problem solving

### THE OBJECTIVE:Learning to handle the math.

Request-Response-Result Is a natural process. Making use of this in problem solving in situations in which mathematics is useful requires learning basic mathematical operations. An important operation is substitution.

The following problem and solution provides an exercise in solving relatively complex problem so far as the mathematical operations are concerned. The ideas that form the basis for the solution are, however, simple and within the reach of anyone.

An algebraic solution was obtained before using the numbers. Thus one has a result that can be use for any rectangular pool/deck. The tendency is to mess with the numbers instead of doing the algebra. Move past solving problems using arithmetic. Algebra works.

There are a number of steps involved in the successive substitution and simplification done above. This provides valuable exercise in mathematical operations.

There are a number of different diagrams that could be used in starting the solution to this problem. The possibilities are shown below.

Solving the problem using these different diagrams provides extensive exercise in geometry and algebra. There are typically several ways to solve a problem. these different ways at their root are the same. They use the same basic ideas but involve differences in details of the steps. Exploring different solutions paths leads to deeper understanding of the problem. The most elegant solution can be discovered. This is the one we show to others.