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MATH WORD PROBLEMS: RACE TO THE FINISH

This guide uses the U.P.S. strategy for individuals to break apart math word problems. This can be used at any time and on any type of math word problem.

INTRODUCTION

Race to the Finish: Thinking Through Difficult Word Problems

Math requires logic and creativity. When perplexities arise, you often have to use complicated strategies to solve a problem. This guide will focus on more challenging problems and methods to solve them.

A RIDDLE

Try this riddle!

Pick any number. Add 4 to it. Multiply the result by 2. Subtract 6 from the result. Divide the result by half. Subtract your original number.

Did you get…1...wow that must be magic. However, it really only involves a little algebra.

  1. Pick a number: x
  2. Add 4: x+4
  3. Multiply by 2: 2(x+4)=2x+8
  4. Subtract 6: 2x+8-6=2x+2
  5. Divide by 2: (2x+2)/2=x+1
  6. Subtract original: x+1-x=…1!

WORKING FORWARD

Once you have organized the information and found a strategy or equation to use, the next step is to find a relationship between the givens. This is often an equation.

See below for an example:

We can also verify that our answer is correct. Logically, it makes sense that a loan at a higher rate and term would have a greater future value. Even though the interest rate is only 0.25% higher, the length of the term causes a significant increase in future value, which means more profit for the lender!

USING LOGICAL REASONING

You may understand the problem. Even then, the problem may require a little more thought. Organizing the given information is only the beginning of the process. Here are the steps:

source

Once you have organized the information, proceed to find logical connections. Look for relevant equations and strategies you have used before. See if you have previously solved a similar, but simple problem.

WORKING BACKWARD

Not all questions require a direct, plug-and-chug relationship. In some cases, you need to manipulate the relationship first. It is important to identify what variable you need to solve for and use algebra to find a direct relationship.

Let us answer another question about the same problem that requires us to work backward.

The most important aspect is to look at the relationship you know and then manipulate it to solve for the variable you are looking for. It is a great idea to brush up on algebra if you are a little rusty.