The formula N=(t^2-t)/2 to find t

Question

The formula N=(t^2-t)/2 (fraction)describes the number of football games, N, that must be played in a league with t teams if each team is to play every other team once. Use this information to find the number of teams that belong to a league which has 36 games scheduled, assuming that each team plays every other team once.

Answer 1

In the formula, N is the number of games and t is the number of teams. We are told that there are 36 games scheduled, so we plug that in for n to get:

 

t²-t = 36

 2

 

Multiply both sides by 2 to get:

 

t²-t = 72

 

Subtract 72 from both sides and you get:

 

t²-t-72 = 0

 

Factor that to get:

 

(t-9)(t+8) = 0

 

That gives us t is either 9 or -8. Since we cannot have a negative number of teams, the answer is 9 teams.