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 isnít 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?


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Last Updated: 9/28/2011
© K. A. Shearer 2005-2011

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