Question

The number of basketball games that must be scheduled in a league with n teams is given by G(n) = (n2 - n)/2 where each team plays every other team exactly once. A league schedules 21 games. How many teams are in the league?

Answer 1

There are 7 teams in the league

Explanation:

Given that the number of games is given by:

`G(n) = ((n^2-n))/(2)`

The equation will be used to determine the number of games. As we already know, that 21 games are scheduled which means G(n) is 21 so we have to find n when G(n) is 21

Putting this mathematically

`21 = (n^2-n)/(2)`

Multiplying equation by 2

`2*21 = 2*(n^2-n)/(2)\\42 = n^2-n\\n^2-n-42 = 0\\n^2-7n+6n-42 = 0\\n(n-7)+6(n-7) = 0\\(n-7)(n+6)=0\\n-7 = 0 => n=7\\n+6=0 => n=-6`

As the number of teams cannot be negative, the number of teams in league are 7.

Hence,

There are 7 teams in the league