Question

10 people are attending a chess tournament, and they are from Team A, Team B and Team C. Every person will complete each of the other 9 contestants. The winner gets 1 point, the loser gets 0 point, and they each get 0.5 points if the game is tied. After the tournament, the average of Team A is 4.5 points, the average of Team B is 3.6 points, and the average of Team C is 9 points. How many members are in Team A, Team B and Team C?

Answer 1

Answer:

Team A = 4 players

Team B = 5 players

Team C = 1 players

Step-by-step explanation:

Each player will compete in nine matches, for a maximum total of nine points possible. Since Team C has an average score of 9, Team C can only have one player because it would be impossible for more than on player to score a nine.

The possible total scores for team B are:

$B =3.6x\\x=1; B=3.6\\x=2; B=7.2\\x=3; B=10.8\\x=4; B=14.4\\x=5; B=18.0\\x=6; B=21.6\\x=7; B=25.2\\x=8; B=28.8\\x=9; B=32.4$

Since the scoring possibilities are 0, 0.5 and 1, total team score must be a multiple of 0.5. Therefore, the only possible number of players for team B is 5 (for a total score of 18.0).

If there are 10 players in total, 5 are from team B and 1 is from team C, the remaining 4 players are part of team A.

Team A = 4 players

Team B = 5 players

Team C = 1 players