Question 1168324: In a basketball league of x teams of which every team plays every other twice, the total number of games played is x²-x
a. How many teams are there in a league the plays a total of 72 games?
b. If there were 6 teams in the league, how many in all would be played?
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
In a basketball league of x teams of which every team plays every other twice,
the total number of games played is x²-x
a. How many teams are there in a league the plays a total of 72 games?
b. If there were 6 teams in the league, how many in all would be played?
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(a) To answer (a), you should find x from this equation
x^2 - x = 72.
Write it in the form x*(x-1) = 72 and guess MENTALLY two consecutive
positive integer numbers giving 72 as the product.
The number x is, OBVIOUSLY, 9.
So, the number of teams on the league is 9.
(b) To answer (b), you simply should substitute x= 6 into the formula.
Next, you need to make an effort and calculate 6^2 - 6,
which, I hope, you can make on your own without my help.
Solved.
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