Question

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 with t chess players. in a round - robin chess tournament, 28 games were played. how many players entered the tournament?
$n=\frac{t^{2}-t}{2}$
how many players entered the tournament?
$square$ players (simplify your answer.)

Explanation:

Step1: Substitute N=28 into formula

$$28 = \frac{t^2 - t}{2}$$

Step2: Multiply both sides by 2

$$28 \times 2 = t^2 - t$$
$$56 = t^2 - t$$

Step3: Rearrange to quadratic equation

$$t^2 - t - 56 = 0$$

Step4: Factor the quadratic

$$(t - 8)(t + 7) = 0$$

Step5: Solve for t

$t - 8 = 0$ or $t + 7 = 0$
$t = 8$ or $t = -7$
Since the number of players cannot be negative, discard $t=-7$.

Answer:

8 players