Question

At the faculty costume party, each teacher from Transylvania Middle School came dressed as his or her favorite creepy creature. The teachers arrived one at a time, and when a new teacher came in, each of the teachers alredy there lined up at the door and shook hands with the newcomer. Count Dracula (Mr. Balb, the math teacher) kept track of the number of handshakes exchanged. He said that there were 171 handshakes exchanged at the party. How many teachers came to the costume party

Answer 1

Let the number of teachers be n
the number of handshakes of n people is
C(n,2)

so C(n,2) = 171
n!/(2!(n-2)!) = 171
n(n-1) = 342
n^2 - n - 342) = 0
(n-19)(n+18) = 0
n = 19 or n= -18, but n > 0

So 19 teachers came

Answer 2

People -19
Handshakes- 18
Total handshakes- 171