Question

If there are x teams in a sports​ league, and all the teams play each other​ twice, a total of​ n(x) games are​ played, where ​n(x)equalsxsquaredminusx. a football league has 7 ​teams, each of which play the others twice. if the league pays ​$45 per​ game, how much will it cost to play the entire​ schedule?

Answer 1

$1,890

Explanation:

Without including repeated instances of games (for instance, if I said that team 4 plays team 2 twice, then that would just be repeating when I already said that team 2 plays team 4 twice):

Team 1 plays:

teams 2, 3, 4, 5, 6, and 7 twice for a total of 12 games

Team 2 plays:

teams 3, 4, 5, 6, and 7 twice for a total of 10 games

Team 3 plays:

teams 4, 5, 6, and 7 twice for a total of 8 games

Team 4 plays:

teams 5, 6, and 7 twice for a total of 6 games

Team 5 plays:

teams 6 and 7 twice for a total of 4 games

Team 6 plays:

team 7 twice for a total of 2 games

--

Total it up:

`12+10+8+6+4+2\\22+8+6+4+2\\30+6+4+2\\36+4+2\\40+2\\42`

Multiply by cost per game.

`42*45=1890`