Question

Please help me solve this word problem:

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, 55 games were played. How many players entered the tournament?

N=t^2-t divided by 2.

Answer 1

t = 11

Explanation:

From the equation that gives, the number of games you can get the number t of players who participated in the ronund-robin tormeo, is:

`N = (t ^ 2-t)/(2)`

`55 = (t ^ 2-t)/(2)`

`110 = t ^ 2-t`

`t ^ 2-t -110 = 0`

`(t-11) (t + 10) = 0`. Then

`t - 11 = 0\\t = 11\\t + 10 = 0\\t = -10`

Since t cannot take negative values, then t = 11.

Answer 2

solve 55=(t^2−t)/2 for t
t2−t=110
t2−t−110=0
(t−11)(t+10)=0


t=11