Peter & Diane have the same average in mathematics. On the next test Diane scored 97% and her aver age improved to 90%, but Peter scored 73% and his average decreased to 87%. How many tests had proceeded this last test?

Answer 1

If there were already n tests, then if Diane scored d and Peter scored p, then with the current average of a,

n*a + 97 = (n+1)(90)
n*a + 73 = (n+1)(87)
so, we can eliminate the a and have

(n+1)(90)-97 = (n+1)(87)-73
(n+1)(3) = 24
n+1 = 8
n = 7