Question

at the conclusion of a party, 36 handshakes are exchanged. Assuming that each guest shook hands with each other others, find the number of guests n at the party.

Answer 1

9 guests

Explanation:

This problem is easily figured if we know the formula for this.

If there are n people in a party and everyone shakes hand with everyone, and the number of handshake exchange is x, the formula is:

`(n(n-1))/(2)=x`

Since x = 36 for this problem, we solve for n:

`(n(n-1))/(2)=x\\(n(n-1))/(2)=36\\n^2-n=72\\n^2-n-72=0\\(n-9)(n+8)=0\\n=-8,9`

n CANNOT be negative, so the number of people is n = 9