Average test grade
This problem often appears on “standardized” tests.
Jane has an average of 87 after 4 tests. What score does she need on the fifth test to average 90 for all five tests?
There are many ways to solve this problem.
1. One is by using algebra.
Let x stand for Jane’s score on the fifth test.
Then
(87*4 + x)/5 = 90
87*4 + x = 450
x = 450 - 348 = 102
Jane needs 102 points, which is impossible, if a test contains at most 100 points!
2. Another way to solve the problem is by using arithmetic.
To average 90 points on 5 tests means to have 450 points. Jane has 348 points, so she needs 102 points.
3. What is the greatest Jane's average can be after test 5? What is the least it can be?
(Let x = 100 for the first question, and let x = 0 for the second question.)
4. A general formula for the average test grade problem.
Let n be the number of exams that have been taken thus far.
Let a be your average on the existing n tests.
Let b be the average that is wanted on n+1 exams.
Let x be the score that you need on the (n+1)st exam to bring your average to b.
Then
a*n + x = b*(n+1)
So
x = b*(n+1) - a*n
In Jane’s case above, n = 4, a = 87, and b = 90.