document.write( "Question 1092322: every two persons shakes hand with each other in a party and the total number of hand shakes is 66.the number of guests in party is \n" ); document.write( "

Algebra.Com's Answer #706921 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "For \"n\" persons the number of hand shakes with each other is    $\"%28n%2A%28n-1%29%29%2F2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So, you need find \"n\" from the equation\r
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\n" ); document.write( "\n" ); document.write( " $\"%28n%2A%28n-1%29%29%2F2\"$ = 66.\r
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\n" ); document.write( "\n" ); document.write( "=====>   n*(n-1) = 2*66 = 132.\r
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\n" ); document.write( "\n" ); document.write( "The only two consecutive positive integers that multiplied to 132 are 11 and 12.\r
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\n" ); document.write( "\n" ); document.write( "So, the answer to your problem is:    The number of guests in the party is 12.\r
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