Application of Linear Equations

We are going to talk about applications to linear equations.  Or, put in other terms, now we will start looking at story problems or word problems. 

Process for Working Story/Word Problems

1.   READ THE PROBLEM.

2.   READ THE PROBLEM AGAIN.  Okay, this might be a little bit of overkill here.

Though, the point of these first two steps is that you have to read the problem. This step is the most important step, however it is also the step that most people don't do correctly.

You need to carefully read the problem and as several times as it takes.  You are only done with this step while you have wholly understood what the problem is asking you to do. It includes identifying all the provided information and identifying what you being asked to determine.

Again, it can't be stressed sufficient that you've to carefully read the problem. Sometimes a single word can totally change how the problem is worked.  If you only skim the problem you may well miss that extremely important word.

3.   Represent one of the unknown quantities along with variable and attempt to associate all the other unknown quantities (if there are any of course) to this variable.

4.   If applicable, sketch a figure reveling the situation. it may seem like a silly step, however it can be incredibly helpful with the next step on occasion.

5.   Make an equation which will relate known quantities to the unknown quantities. In order to does this make use of known formulas and frequently the figure sketched in the previous step can be used to make the equation.

6.   Solve out the equation formed in the previous step and write the answer to all the questions.  It is significant to answer all the questions which you were asked.  Generally you will be asked for many quantities in the answer and the equation will only give one of them.

7.   Check your answer. Do this through plugging into the equation; however also use intuition to ensure that the answer makes sense.  Mistakes can frequently be identified by acknowledging that the answer doesn't just make sense.

Let's begin things off with a couple of fairly fundamental examples to illustrate the procedure.  Note as well that at this point it is supposed that you are able of solving fairly simple linear equations and hence not much detail will be given for the real solution stage. The instance of this section is more on the set up of the equation than the solving of the equation.