Answer:
9 guests
Step-by-step 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:
[tex]\frac{n(n-1)}{2}=x[/tex]
Since x = 36 for this problem, we solve for n:
[tex]\frac{n(n-1)}{2}=x\\\frac{n(n-1)}{2}=36\\n^2-n=72\\n^2-n-72=0\\(n-9)(n+8)=0\\n=-8,9[/tex]
n CANNOT be negative, so the number of people is n = 9
