Question

In a statewide soccer competition, 36 games were played. Each team participating in the competition played once with every other team. How many teams participated in the statewide competition?

Answer 1

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.

Answer 2

The number of teams participated in the statewide competition is $\boxed{9{\text{ teams}}}.$

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,

$\begin{aligned}{\text{Number of matches}} &= 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8\\&= 36\\\end{aligned}$

The number of teams participated in the statewide competition is $\boxed{9{\text{ teams}}}.$

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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.