Question 1168324
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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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<pre>
(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.
</pre>

Solved.