SOLUTION: Hi. Can you help me solve this? I'm stuck. How many teams are in a league that schedules 45 games in such a way that each team plays every other team only once? Thanks.

Question 682506: Hi. Can you help me solve this? I'm stuck.
How many teams are in a league that schedules 45 games in such a way that each team plays every other team only once?
Thanks.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let x = number of teams in the league. Since each game includes 2 teams, you are looking for a COMBINATION problem, C(x,2) = 45.

In other words,

Now, if you are an algebra student, you should multiply out the left side to obtain x^2 - x = 90, and solve the quadratic equation.
x^2 - x - 90 = 0
(x-10)(x+9)=0
x= 10 or x=-9, reject the negative answer. There are 10 teams in the league.

If you are a statistics student, you should ask yourself, what number times one more that the number would give you a product of 90. Probably pretty obvious that the numbers would be 9 and 10.

To analyze the answer, what you have is 10 teams in the league, and each team has 9 opponents. Lest you think this gives you 90 games, remember that Team A playing Team B is the same as Team B playing Team A, so you have to divide by 2 in order to eliminate the duplication of games.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

P.S. Check out my website for full color explanations and lots of practice tests with detailed solutions for all levels of math at www.mathinlivingcolor.com.
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