Question 1182520: Four teams play in a soccer tournament. Each team plays one game against each of the other three teams. Teams earn 3 points for a win, 1 point for a draw and 0 points for a loss. After all the games have been played, one team has 6 points, two teams have 4 points and one team has 3 points. How many games ended in a draw?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
With four teams each playing each other team once, there were C(4,2)=6 games played.
For each game in which one team won, a total of 3+0=3 points were awarded; for each game that ended in a draw, a total of 1+1=2 points were awarded.
The total points awarded were 6+4+4+3 = 17.
Informally, 6 integers each either 2 or 3 with a sum of 17 means five 3's and one 2, meaning one game ended in a draw.
ANSWER: 1 game ended in a draw.
Formally....
Let x be the number of games that ended in a draw
Let y be the number of games in which one team won
[1] x+y=6
[2] 2x+3y=17
[3] 3x+3y=18 [1], times 3
[4] x=1 [3] minus [2]
ANSWER: The number of games that ended in a draw was x=1.
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