SOLUTION: In a​ round-robin chess​ tournament, each player is paired with every other player once. The​ function, shown​ below, models the number of chess​ game

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Question 1066884: In a​ round-robin chess​ tournament, each player is paired with every other player once. The​ function, shown​ below, models the number of chess​ games, N, that must be played in a​ round-robin tournament with t chess players. In a​ round-robin chess​ tournament, 6 games were played. How many players entered the​tournament?
how to solve formula? N=t^2-t / 2
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!



Replace N with 6. The goal is to solve for t.


Multiply both sides by 2





Subtract 12 from both sides








Factor


or


or


Ignore the negative solution since it makes no sense to have -3 players.


The only practical solution is


There are 4 players in the tournament.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
In a​ round-robin chess​ tournament, each player is paired with every other player once.
The​ function, shown​ below, models the number of chess​ games, N, that must be played in a​
round-robin tournament with t chess players. In a​ round-robin chess​ tournament, 6 games were played.
How many players entered the​tournament?
how to solve formula? N=t^2-t / 2
~~~~~~~~~~~~~~~~~~~~~~ 

You need to solve the equation  = 6.

Multiply both sides by 2. You will get an equivalent equations

 = 12,

 = 0,

(t-4)*(t+3) = 0.

The roots are t= 4 and t= -3.

Since you need integer positive solution, the only one is t= 4.


Answer. 4 players.


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