Word Problem Discussion
Often we find that we can measure the world in seemingly very different ways, only to find that, as we vary the objects being measured, the measurements themselves vary in related and predictable ways. Such predictions are exactly what interests us in this course.Let us Consider three examples.
Let us examine the organization of possible data for the above example. As we recorded heights and weights, we wrote the person's name on one line and then recorded that person's height and weight on the same line as we measured them. It is vital that the heights and weights be thus paired. If someone took the list and randomly mixed up the heights and weights of people, no relationship could then be found between height and weight. The fact that a pair of numbers, like a person's height and weight, are different aspects of a single object or event is the reason that we consider representing such a pair as a single point in a two dimensional x,y plane. Similarly, recognizing this inseparable pairing in a word problem crucial to beginning the problem, much less solving it.
The proceedure necessary to attack a linear word problem then, is to first identify the units of the two important measurements in the problem. In the last sample, the rate problem, the units are hours and miles. More specifically, the measurements are the number of hours that we drove the car and the number of miles that the car was driven. In example 1 above, both units are dollars. One is the number of dollars that the item costs and the other is the number of dollars that we must charge for sales tax.
Test yourself by chosing the units of example 2 from below: