Twenty-eight games were played in a football tournament with each team playing once against each other. How many teams were there?

Explanation

Let number of teams be n.
Number of matches to be played
= number of ways two teams can be selected
`= .^(n)C_(2)=28`
`therefore (n(n-1))/(2)=28`
`implies n^(2)-n-56=0`
`implies (n-8)(n+7)=0`
`implies n=8 " as" n ne -7`.