Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 22. Eight teams participate in a football tournament. Each team plays each other exactly once.  In each match, the winner earns three points, and the loser does not earn any points. If the match is a draw, each team earns one point.  At the end of the tournament, the total number of points earned by all the teams is 61. What is the largest number of points that the champion team could have earned?  To solve this question, we will take the number of teams multiplied by the number of games they played, 8 and 7, divided by 2 times 1. This will give us 56 divided by 2, or 28.  Next, we have to look at wins and draws. A win means three more total points, and a draw means two more total points to the whole pool of 61.  So, we can set up an equation of 61 equal to 3W, or wins, plus the difference of 28 and W, multiplied by 2.  This means the amount of games that ended with draws, and we multiply by 2, since a draw results in two points.  We simplify this into 61 equal to 3W plus 56 minus 2W, or 61 equal to W plus 56, or W equals 5. So, the team had 5 wins. 5 times 3 equals 15.  The other two games of this team have ended in draws, so we add 1 and add 1. And with this, we do 15 plus 1 plus 1 to get our solution, which is D, 17.

Video Summary

In a football tournament with eight teams, each team plays the others once, totaling 28 matches. With each win earning three points and each draw two (split between both teams), the total points from all matches were 61. To find the maximum points for the champion team, the breakdown is 5 wins (earning 15 points) and 2 draws (adding 2 points). Thus, the maximum points the champion team can earn is 17. This solution results from setting up an equation accounting for wins and draws, and solving for the number of winning games.

Keywords

football tournament

maximum points

champion team

match points

tournament format