document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #807519 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "If \"n\" is the number of persons, and if each shakes hand with every other person,\r\n" );
document.write( "\r\n" );
document.write( "then the number of handshakes is  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, you have this equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = 36,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which gives\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    n*(n-1) = 2*36 = 72;\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "hence,  n = 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  There are 9 persons at the party.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );