### If you take the time to understand the solution of this problem then you will know how to solve all problems.

Those familiar with introductory algebra will recognize that word problems consist of several conditions that must simultaneously be satisfied. The methods of solving simultaneous equations are then appropriate. Here the common method of elimination by substitution is used. The four simultaneous equations are written. Then the substitutions are done. The process uses mathematics to do mathematics, providing a unified approach to problem solving that spans the curriculum.

### Mathematics provides a real way to solve real problems. Learn to use mathematics for problem solving.

The solution starts by responding to what is ASKED FOR: How many does Mary have if she has two more than Tom? One condition.

The starting equation REQUESTS information about the number of apples Tom has. This is stated as 3 times the number Susan has. A second condition.

The resulting equation REQUESTS information about how many apples Susan has. This is stated in the problem as one fourth the number Joe has. A third condition.

Now information is requested about the number of apples Joe has. The problem states that Joe has 4 apples. The fourth condition.

The REQUEST-RESPONSE-RESULT structure is used repeatedly in solving problems.

Solving simultaneous equations is formally introduced as a separate, unrelated topic in algebra and is therefore feared. Yet we use the idea of satisfying simultaneous conditions in our daily lives in a quite natural way, beginning in childhood. Recognizing mathematics as a natural language will do much toward making it a useful language to a broad population.

See complete solution of the Cat/Train problem.
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