Santa’s mathmatics teacher has given the class five tests this semester, each scored from 0 to 100 inclusive. Senta had an average of 90 for the five tests. What was the lowest possible score Senta could have earned on any one test?
Students usually begin a problem of this type by using trial and error in an attempt to find Senta’s lowest possible score. However, this procedure does not guarantee finding it.
Let’s consider the extreme case. If Senta had an overall average of 90 for the five tests, the total of her scores must be 5 x 90 = 450. Now, consider the extreme (highest) possible score for each of the first four tests, namely, 100 for each. This is a total of 400. Thus, the lowest possible score one test for Senta would have been 50, so as to achieve the total 450.