The number of participants in the game is 11
Represent the number of games with n.
The equation that represents the total number of games is the sum of nth of a sequence
[tex]S_n = \frac{n * (n - 1)}2[/tex]
So, we have:
[tex]66 = \frac{n * (n - 1)}2[/tex]
Multiply both sides 2
[tex]132 = n * (n - 1)[/tex]
Expand the bracket
[tex]132 = n^2 - n[/tex]
Rewrite as:
[tex]n^2 - n - 132 = 0[/tex]
Expand
[tex]n^2 +12n -11 n - 132 = 0[/tex]
Expand
[tex]n(n +12) -11 (n + 12) = 0[/tex]
Factor out n + 12
[tex](n -11) (n + 12) = 0[/tex]
Solve for n
n = 11 or n = -12
n cannot be negative.
So, we have:
n = 11
Hence, the number of participants is 11
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