To celebrate "New Year's Day", the city trade union organized a basketball game. The competition system was a single round-robin format (every two teams played one game). *** played 45 games. This tim

To celebrate "New Year's Day", the city trade union organized a basketball game. The competition system was a single round-robin format (every two teams played one game). *** played 45 games. This time there were __

10

Suppose there are x teams participating in the game this time. Since the competition system is a single round-robin format (every two teams play one game), then the total number of games in this game For: field. According to the meaning of the question, we can know that the total number of games in this competition = 45 games. According to this equivalent relationship, just list the equations and solve them.

Solution: Suppose there is team >

After sorting, we get: x 2 -x-90=0,

The solution is: x 1 =10, x 2 =-9 (discard if it does not meet the meaning of the question),

So, there are 10 teams participating in the competition this time.

Answer: There are 10 teams participating in the competition this time.

The key to this question is to clearly understand the meaning of the question, find the appropriate equivalence relationship, list the equation, and then solve it. It should be noted that the competition format is a "single round-robin format", and the total number of games between pairs must be divided by 2.