Question

The number of volleyball games that must be scheduled in a league with n teams is given by G(n) = `("n"^2 - "n")/2` where each team plays with every other team exactly once. A league schedules 15 games. How many teams are in the league?

Answer 1

Number of games = 15

G(n) = `("n"^2 - "n")/2` 

`("n"^2 - "n")/2` = 15

n² – n = 30

⇒ n² – n – 30 = 0

⇒ n² – 6n – 5n – 30 = 0

(n – 6) (n + 5) = 0

n – 6 = 0 or n + 5 = 0 ...[Note: – 5 is neglected because number of team is not negative]

n = 6 or n = – 5

∴ Number of teams = 6