Question

In a local basketball league championship total 198 games were played, where each team played exactly three games with all the other teams. How many teams participated in this championship?

Answer 1

12

Explanation:

When n teams play each other once, the total number of games is n(n-1)/2. Since each team played every other one 3 times, the relationship between number of teams (n) and number of games is ...

3(n(n-1)/2) = 198

n(n-1) = 132 = 12·11 . . . . . . multiply by 2/3 and factor

n = 12 . . . . . . n = -11 is also an extraneous solution to this quadratic equation

12 teams participated in this championship.