We need to talk about applications to linear equations. Or, put in other words, we will now start looking at story problems or word problems. Throughout history students have hated these. It is my belief however that the main reason for this is that students really don’t know how to work them. Once you understand how to work them, you’ll probably find that they aren’t as bad as they may seem on occasion.
Process for Working Story/Word Problems
- READ THE PROBLEM.
- READ THE PROBLEM AGAIN. Okay, this may be a little bit of overkill here. However, the point of these first two steps is that you must read the problem. This step is the MOST important step, but it is also the step that most people don’t do properly.
You need to read the problem very carefully and as many times as it takes. You are only done with this step when you have completely understood what the problem is asking you to do. This includes identifying all the given information and identifying what you being asked to find.
Again, it can’t be stressed enough that you’ve got to carefully read the problem. Sometimes a single word can completely change how the problem is worked. If you just skim the problem you may well miss that very important word.
- Represent one of the unknown quantities with a variable and try to relate all the other unknown quantities (if there are any of course) to this variable.
- If applicable, sketch a figure illustrating the situation. This may seem like a silly step, but it can be incredibly helpful with the next step on occasion.
- Form an equation that will relate known quantities to the unknown quantities. To do this make use of known formulas and often the figure sketched in the previous step can be used to determine the equation.
- Solve the equation formed in the previous step and write down the answer to all the questions. It is important to answer all the questions that you were asked. Often you will be asked for several quantities in the answer and the equation will only give one of them.
- Check your answer. Do this by plugging into the equation, but also use intuition to make sure that the answer makes sense. Mistakes can often be identified by acknowledging that the answer just doesn’t make sense.
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