Difference between revisions of "1997 AHSME Problems/Problem 11"
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Revision as of 22:02, 8 August 2011
Problem
In the sixth, seventh, eighth, and ninth basketball games of the season, a player scored ,, , and points, respectively. Her points-per-game average was higher after nine games than it was after the first five games. If her average after ten games was greater than , what is the least number of points she could have scored in the tenth game?
Solution
The sum of the scores for games through is . The average in these four games is .
The total points in all ten games is greater than . Thus, it must be at least .
There are at least points in the other six games: games and game .
Games must have an average of less than . Thus we cannot put more than points in those five games.
Thus, the tenth game must have at least points, and the answer is .