Setting Up to Solve Story Problems in Algebra

When solving story problems, the equation you should use or how all the ingredients interact isn't always immediately apparent. Sometimes you have to come up with a game plan to get you started. Just getting started can be a big help. You don't have to use every suggestion in the following list with every problem, but using as many as possible can make the task more manageable.

• Draw a picture. It doesn't have to be particularly lovely or artistic. Many folks respond well to visual stimuli, and a picture can act as one.

• Assign a variable(s) to represent how many or number of. You may use more than one variable at first and refine the problem to just one variable later. Remember, a variable can represent only a number; it can't stand in for a person, place, or thing.

• If you use more than one variable, go back and substitute known relationships for the extra variables. When it comes to solving the equations, you want to solve for just one variable. You can often rewrite all the variables in terms of just one of them. For example, if you let a represent the number of Ernie's cookies and b represent Bert's cookies, but you know that Ernie has four more cookies than Bert, then a can be replaced with b+4.

• Look at the end of the question or problem. This often gives a big clue as to what is being asked for and what the variables should represent. It can also give a clue as to what formula to use, if a formula is appropriate.

• Translate the words into an equation. Replace

• and, more than, exceeded by with the plus sign

• less than, less, subtract from with the minus sign

• of, times as much with the multiplication sign

• twice with 2x

• divided by with the division sign

• half as much with 1/2 x

• the verb (is and are, for example) with the equal sign

• Plug in a standard formula, if the problem lends itself to one.

• Draw a picture of containers when doing mixture problems. Label each container with a quantity times a quality. The quality is the strength of the solution or percent interest or price per pound of the item.

After you get set up, you're ready to solve the equation. Make sure to check your answer for sense as well as accuracy. Ask yourself whether the answer makes sense in this situation.