Question

A group of friends shook hands with each other at a party. Peter did notshake hands with everyone at the party because he was late and somefriends had already left. There were a total of 25 handshakes. How many friends were still at the party when Peter arrived?

Answer 1

When "n" number of people then number of people is:

`\text{handshakes}=(n(n-1))/(2)`

If the handshakes is 25 then:

`25=(n(n-1))/(2)`
`\begin{gathered} 25*2=n(n-1) \\ 50=n^2-n \\ n^2-n-50=0 \\ \end{gathered}`

Solve the equation:

`\begin{gathered} n=\frac{-(-1)\pm\sqrt[]{1-4(1)(-50)}}{2} \\ n=\frac{1\pm\sqrt[]{1+200}}{2} \\ n\approx7 \end{gathered}`

So 7 friends still at the party.