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 is given by N = n^2

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 is given by N = n^2 - n. How many teams are in a softball le

Question 173198This question is from textbook Introductory Algebra
: 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 is given by 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 Introductory Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"if the total number of games played is 42", this means that

Start with the given equation

Plug in

Subtract 42 from both sides.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for n

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, you cannot have a negative number of teams. So this means that the only solution is

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Answer:

So the solution is which means that there are 7 teams in the league.
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