#  Solving word problems

## Getting rid of the words

1. Draw a picture

Most problems are easier to solve if you can draw a picture. It doesn't have to be pretty, jus close enough to help you.

Label your picture with symbols, numbers, or names that help you make sense of the words. Fill it in more or change the drawing as you set up an equation for the problem.

2. Translate conjunctions and verbs

To help get rid of the words, you need to use clues from the problem to help you set up an equation by translating words into math symbols. Some examples are:

 Math symbol Common words plus + and, increased by, more than minus - less than, decreased by, taken away 2 times  2x twice, double equal = are, has, is, same as

3. Assign variables to represent numbers

Use variables (letters) to represent unknown numbers. Pick letters that can help you make sense of the problem. For example, if you are trying to find a height, you might call it h.

4. Look at the last sentence

The last sentence of the problem usually is where the question is stated. It might use words like "what is" or "how many".

5. Find a formula

Depending on the question in the problem, you might be able to use a standard formula for area, distance, interest, and so on. When possible, use a standard formula for your equation or as part of your equation.

In many algebra problems, you have to make up your own formula based on the problem. Sometimes these are combined with standard formulas.

6. Simplify by Substituting

Look for variables with relationships to another variable and try to express one of those variables in terms of the other.
For example, if one side of a rectangle is twice as long as the other side, you can use x and 2x to represent the two sides rather than x and y. The fewer letters (variables) in your problem, the easier it is to solve.

7. Solve an Equation

Translate the word problem into an equation that represents the situation and relationships expressed in the problem. Solve the equation carefully using the rules of algebra.

8. Check for Sense

When you get an answer, decide if it makes sense in the context of the word problem. If the answer makes sense, it still might not be the correct answer, but it is the first check to tell if it isn’t correct.

Also remember that word problems frequently use units of measure, like feet, inches, miles and so on. For your answer to make sense, you need to have the correct units in your answer.

9. Check for Accuracy

If the answer makes sense, then check for accuracy by substituting the answer back into your equation and checking the algebra.

Example

Your piggy bank only has dimes and nickles. If there are 52 coins in the bank and there are three times as many dimes as nickles, how much money is in the bank?

• Let d stand for the number of dimes
• Let n stand for the number of nickles
• Since there are 52 dimes and nickles together d + n = 53
• Because there are 3 times as many dimes as nickles, d = 3n
• Now I can substitute for d and get 3n + n =52 or simplified to 4n = 52
• Dividing by 4 I get n = 13 so I know there are 13 nickles
• Since nickles plus dimes equals 52, dimes must be 52 - 13 or 39 dimes
• You need three times as many dimes as nickles. Since 13 nickles times 3 equals 39 dimes, this part makes sense to me
• To find how much money I will take 13 nickles times 0.05 cents to get 0.65 cents
and 39 dimes times 0.10 cents to get \$3.90
for a total of \$0.65 + \$3.90 = \$4.55

Comments, questions, or you just need some help? Send an e-mail to Mrs. Shearer Last Updated: 9/28/2011