Solve the problem.
-Within a group of $n$ people, the number of possible handshakes, $N$, is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$. At a party, everybody shakes hands with every other person. If the total number of handshakes is 253 , how many people are at the party?
A) 24
B) 22
C) 25
D) 23

Question

Quizplus · Accepted Answer

Given the formula for the number of handshakes is $N = \frac{1}{2}(n^2 - n)$, and $N = 253$, we solve for $n$: $506 = n^2 - n$. Rearranging gives $n^2 - n - 506 = 0$. Factoring or using the quadratic formula, we find $n = 23$ or $n = -22$. Since the number of people cannot be negative, $n = 23$ is the correct answer.

Solve the Problem nnn People, the Number of Possible Handshakes NNN , Is Given By

Solve the Problem $n$ People, the Number of Possible Handshakes $N$ , Is Given By