Answer to September 25, 2000 Problem

The Test Problem

 
A certain calculus teacher uses the following grading formula to determine a student's grade:
He averages all the tests together and calls that the Test average.
He averages all the quizzes together and calls that the Quiz average.
He figures the student's grade by the formula:
Grade = (2 * Test Average + Quiz Average) / 3

After 3 tests and 2 quizzes, the student's Test Average is 83 and her Quiz Average is 89. What did she get on her 4th test if her overall grade dropped to an 83?

P.S. Can you give a general formula for this situation? That is, given the previous Test Average (T), previous Quiz Average (Q), the number of previous tests (N), and the new overall grade (G), what mark (M) must the student have gotten on the next test?

 

Solution to Problem:

Answer is 71.

Solution:
For an overall grade of 83, and a quiz average of 89, the student must have an 80 test average. Since the student had an 83 test average before, she must have gotten a 71 on the next test:
(3 * 83 + M)/4 = 80

The general formula would be:
M = ( (N+1)(3G - Q) - (2NT) ) / 2

So in the problem above, where N = 3, G = 83, Q = 89, and T = 83,
M = ( (3+1)(3*83 - 89) - (2*3*83) ) /2 = 71


Correctly solved by:

1. Erin McGinnis Winchester, VA
2. Bob Hearn Winchester, VA
3. Elizabeth Cotter Oak Hill, VA
4. Richard Mocarski Virginia Tech
5. Kirstine Wynn Winchester, VA
6. Chad McDaniel Winchester, VA
7. Cathrine Roby Winchester, VA