Before taking his last test in a class, the arithmetic mean of Brians's test scores is 91. He
has determined that if he scores 98 on his last test, the arithmetic mean of all his test scores
will be exactly 92. How many tests, including the last test, does Brian take for this class?
Let n = number of tests already taken.
Then, n + 1 will be the total number of tests, including the final test.
Since his average is 91, the total number of points that he has, so far, is 91·n.
If he gets a 98 on his final test, he will then have 91n + 98 points.
At that time, to find his average, divide this amount by n + 1.
So: (91n + 98) / (n + 1) = 92
Multiplying both sides by n + 1: 91n + 98 = 92(n + 1)
Simplify: 91n + 98 = 92n + 92
Subtract 91 n from both sides: 98 = n + 92
Subtract 92 from both sides: 6 = n
The total number of tests, including the final is: n + 1 = 7.