How to Write Linear Equation Word Problems

Writing your own linear equation word problems for your students can make the math assignment not only more fun for the kids, but can make it more relevant. In writing your own problems, you can use scenarios from everyday life that the kids will likely encounter. Moreover, you can use your students' names to personalize the work. When kids see that math is relevant, they begin to understand math's importance in their lives. The process of writing a simple word problem, requiring a pair of linear equations using two variables, is really a simple matter.

Instructions

1. Choose a scenario. Perhaps your scenario will have to do with how many steps a marching band marches. Or maybe your scenario deals with fund-raising for the prom. You could write a problem about car washes or candy sales or the number of touchdowns and field goals. If your students have part-time jobs after school, you could write problems dealing with wages and number of hours worked. Maybe your students are saving to buy a car, and a problem about car payments would be relevant.

2. Decide if your problem will have one or two variables. Remember, for each variable, you will need to write an equation. So if there are two variables to solve for, you will need two equations.

3. Work backwards. Start with those values that will be the coefficient(s) and the answer(s) to your variable(s). For example, keeping with simple values, say you have Cindy and Maria washing cars to raise money for the prom. You can write a series of word problems on this theme, with one problem having to do with the money raised, another with the number of cars washed, or how long Cindy and Maria worked. For this example, we will use number of cars washed for each girl as the variables. The answers will be that Maria washed 10 cars, and Cindy washed 3.

4. Establish the basic information the student will seek. Using the numbers 10 and 3 as the outcomes, come up with a way to state the variables. The obvious would be that the number of cars Cindy and Maria washed together was 13. This results in a very simple C + M = 13. Something less obvious as a starter equation might be, if Cindy had washed 2 more cars, then she would have washed exactly half the number of cars Maria washed. Or to rephrase it, Maria would have washed exactly twice the number of cars Cindy washed if Cindy washed 2 more cars. These statements would result in equations like C + 2 = 1/2 x M or C + 2 = M/2 or M = 2(C + 2).
   You can use the very simple and the less simple as your two equations, and you are finished.

5. Use either the simple first equation or one of the second-version equations and pair your linear equation with some more information. So alternatively, you could say that Cindy spent 1 hour on each of the cars she washed, whereas Maria spent only 30 minutes on each car. If you added together the number of hours the girls washed cars, it would total to 8 hours. This information can give you your second equation of M/2 + C = 8.
   Using this statement will require your students to realize that 30 minutes is half an hour, although it is possible you will have students who come up with the equation 30M + 60C = 480 (which will also work).

6. Write your finished problem, scattering the information. Here's our example: Cindy and Maria are washing cars to raise money for the prom. Together, they washed cars for 8 hours. During that time, Maria would have washed exactly twice as many cars as Cindy, if Cindy had washed two more cars. The reason Maria washed more cars was because she worked faster than Cindy, spending only 30 minutes to wash a car, while Cindy spent an hour on each car. How many cars did Maria and Cindy each wash?
   Your equations are M = 2(C + 2) and M/2 + C = 8.

Resources

• Algebra Lab