Answer:
9 teams
Step-by-step explanation:
If the total games played was 36 and no team played each other twice, we need to ensure there isn't any double counting.
36 = (n-1) + (n-2) + (n-3) ... + (n-(n-1))
using this knowledge, we can then count up:
1+2+3+4+5+6+7+8 = 36
If our highest number is 8, then we know there must be 9 teams, because no team can play themselves.
The number of teams participated in the statewide competition is [tex]\boxed{9{\text{ teams}}}.[/tex]
Further explanation:
Given:
In a statewide soccer competition, 36 games were played.
Each team participating in the competition played once with every other team.
Explanation:
No team will play 2 matches with the second team.
There are 36 games played in the statewide competition.
The number of teams participated in the statewide competition can be obtained as follows,
[tex]\begin{aligned}{\text{Number of matches}} &= 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8\\&= 36\\\end{aligned}[/tex]
The number of teams participated in the statewide competition is [tex]\boxed{9{\text{ teams}}}.[/tex]
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter:Number System
Keywords: statewide, soccer, competition, 36 games, played, teams participating, statewide competition.
