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 28 , how many people are at the party?
A) 8
B) 10
C) 7
D) 9

Question

Quizplus · Accepted Answer

The formula for the number of handshakes is $N = \frac{1}{2}(n^2 - n)$. Setting $N = 28$, we solve $\frac{1}{2}(n^2 - n) = 28$. This simplifies to $n^2 - n = 56$. Solving the quadratic equation $n^2 - n - 56 = 0$ gives $n = 8$ or $n = -7$. Since the number of people cannot be negative, $n = 8$.

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