Answer: 15 teams
Step-by-step explanation:
Total number of games played in the tournament = 105
Number of participating teams = p
Each team plays against every other team , then the total number of games played by each team = (p - 1) , since a team can't play itself
To obtain total number of games played =
(Number of teams × number of games played) [p × (p-1)]
However, the teams played against each other only once :
Therefore, total number of games played:
[p × (p-1)] / 2
Since we've been given the total number of games played :
[p × (p-1)] / 2 = 105
p × (p-1) = 105 × 2
p × (p-1) = 210
p^2 - p = 210
p^2 - p - 210 = 0
p^2 - 15p + 14p - 210 = 0
p(p - 15) +14(p-15) = 0
(p - 15) = 0 or (p + 14) = 0
p = 15 or p = - 14
Number of teams can't be negative
Therefore p = 15
Number of teams = 15
