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?

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(52780) (Show Source): You can put this solution on YOUR website!
.


If "n" is the number of persons, and if each shakes hand with every other person,

then the number of handshakes is  .


So, you have this equation


     = 36,


which gives


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


hence,  n = 9.


ANSWER.  There are 9 persons at the party.

Solved.

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