suppose that 10 teams participated in a soccer tournament where each
team played exactly one game with each of the other teams. The winner
of each game received 3 points, while the loser received 0 points. In case
of a tie, both teams received 1 point. At the end of the tournament, the
10 teams received a total of 130 points. How many games ended in a tie? Select:
A) 1  B) 2  C) 3  D) 4  E) 5
There were 45 games played in the tournament (10 2 )games.   Now, the total   number of points awarded in one game is either 3 (if one team wins), or 2 (when the   teams tie the game). So, the total number of points received is 3 × 45−(the number of   games ended in a tie). Thus, exactly 5 games ended in a tie.   correct answer 5
<result>E</result>
suppose that 10 teams participated in a soccer tournament where each
team played exactly one game with each of the other teams. The winner
of each game received 3 points, while the loser received 0 points. In case
of a tie, both teams received 1 point. At the end of the tournament, the
10 teams received a total of 130 points. How many games ended in a tie?