Her point average must be 30 per game for the remaining games.
Explanation
Suppose, the total number of games in the season is [tex]x[/tex]
As the average of all games for the season is 22 points per game, so the total points in all games = [tex]22x[/tex]
Now, two-thirds way of the season, the average is 18 points per game. That means, for [tex]\frac{2x}{3}[/tex] number of games, the average is 18 points per game.
So, the total points in [tex]\frac{2x}{3}[/tex] number of games [tex]= \frac{2x}{3}*18= 12x[/tex]
Now the number of remaining games [tex]= x- \frac{2x}{3}= \frac{x}{3}[/tex] and the total points in these remaining games [tex]= 22x-12x= 10x[/tex]
So, the average for the remaining games [tex]= \frac{10x}{\frac{x}{3}}= \frac{30x}{x}= 30[/tex] per game.
