SOLUTION: In a birthday party, each person shakes hand with every other person. If there was a total of 36 handshakes in the party, how many persons were present in the party?

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Question 1178310: In a birthday party, each person shakes hand with every other person. If there was a total of 36 handshakes in the party, how many persons were present in the party?
Answer by ikleyn(52778) About Me  (Show Source):
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If "n" is the number of persons, and if each shakes hand with every other person,

then the number of handshakes is  %28n%2A%28n-1%29%29%2F2.


So, you have this equation


    %28n%2A%28n-1%29%29%2F2 = 36,


which gives


    n*(n-1) = 2*36 = 72;


hence,  n = 9.


ANSWER.  There are 9 persons at the party.

Solved.