At a party, everyone shook hands with everyone else. there were 66 handshakes. how many people were at the party? explain.

N-the number of people
The first person shake n-1 hands, the second n-2the last person shake one hand

1+2+3++n-1=n*(n-1)/2=66
⇒ n*(n-1)=66*2=132=12*11
⇒ n=12 people was at the party

143 75 107 13 the answer