Answer to September 27, 1999 Problem

A Little Average Problem
adapted from a problem
in issue #91 of Recreational & Educational Computing

In the 6th, 7th, 8th, and 9th basketball games of the season, Mary scored 23, 14, 11, and 20 points, respectively. Her points-per-game average was higher after 9 games than it was after the first 5 games. If her average after 10 games was greater than 18, what is the least number of points she could have scored in the 10th game?

Answer to the Problem:

The least number of points Mary could have scored was 29.

For an average of 10 points to exceed 18 points, there must be at least 181 points. Thus 181 points is our target...

Mary scored a total of 68 points in games 6 through 9, which is a 17 point avarage.
In order to score least in game 10, Mary must score as much as possible in the first 5 games, but without violating the stated requirement that her average after 9 games was higher than after 5 games.

This means she must average just a little less than the 17 point average that she had in the last 4 games (games 6 through 9).
So, assign 17 points for all but 1 of the first 5 games, and then 16 for the other game. So, she totalled 84 points in the first 5 games. The total for the first 9 games is then 68 + 84 = 152.

To get the least number of points in game #10, she needs
181 (target) - 152 (number so far) = 29 points.


Correctly solved by:

1. Jon Pence Winchester, VA
2. Chip Crawford Winchester, VA