SOLUTION: 7 teams are in the Christmas Basketball Tournament. Each team will play each other only once. ~ graph a network of the tournament ~ how many games were played in total? ~ if 2

Algebra ->  Length-and-distance -> SOLUTION: 7 teams are in the Christmas Basketball Tournament. Each team will play each other only once. ~ graph a network of the tournament ~ how many games were played in total? ~ if 2      Log On


   

Question 731820: 7 teams are in the Christmas Basketball Tournament. Each team will play each other only once.
~ graph a network of the tournament
~ how many games were played in total?
~ if 2 more teams were added to the tournament list, how many games would then be played?
~ show your work and explain your answer
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53595) About Me  (Show Source):
You can put this solution on YOUR website!
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7 teams are in the Christmas Basketball Tournament. Each team will play each other only once.
~ graph a network of the tournament
~ how many games were played in total?
~ if 2 more teams were added to the tournament list, how many games would then be played?
~ show your work and explain your answer
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Each of 7 teams plays with each of 6 teams.

So, our first wish is to multiply 7 by 6 and to get 42.


But then a brilliant thought comes to our mind: it tells that doing this way,
we count each play twice. 
 
Therefore, we divide 42 by 2 and get the correct  ANSWER  42%2F2 = highlight%28highlight%2821%29%29.


If 2 more teams were added, when we calculate similarly: we multiply 7+2 = 9 by 9-1=8

    9*8 = 72,

and then divide by 2 to get the  ANSWER  highlight%28highlight%2836%29%29.

Solved (without making a graph of network, which is the job bordering with madness).