SOLUTION: In a sports league of n teams in which each team plays every other team twice, the total number n of games to be played in given N=n^2-n. How many teams are in a softball league if

Question 187440This question is from textbook
: In a sports league of n teams in which each team plays every other team twice, the total number n of games to be played in given N=n^2-n. How many teams are in a softball league if the total number of games played is 42? This question is from textbook

Answer by feliz1965(151) (Show Source): You can put this solution on YOUR website!
Let N = 42
42 = n^2 - n
Subtract 42 from both sides.
n^2 - n - 42 = 0
We now have a quadratic equation.
The left side becomes (n - 7)(n + 6) and we set it to = 0
Set each factor equal 0 and solve for n.
n - 7 = 0
n = 7
========================================
n + 6 = 0
n = -6
We reject the answer n = -6 because there is no such thing as a total of negative games.
The answer is n = 7.

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