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At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

 Jun 19, 2020
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Let the number of people be x. Each person shakes with x-1 people (everyone but themselves).

Since there are x people, there are x(x-1)/2 handshakes. We have to divide by 2 because we counted both of the people that are shaking hands. 

From the problem, we know that x(x-1)/2 = 66. Multiply both sides by 2 to get x(x-1) = 132. 

132 = 12*11, so x = 12

 Jun 19, 2020

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