SOLUTION: n people shake hands at the start of a meeting. If there are 36 handshakes in all, find the value of n.

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Question 762132: n people shake hands at the start of a meeting. If there are 36 handshakes in all, find the value of n.
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Number of handshakes = the number of ways you can choose 2 people from a set of n (each set of 2 people will have 1 handshake)
In combinatorial terms this is C(n,2) or n%2A%28n-1%29%2F2%7D%7D%0D%0A%0D%0A%7B%7B%7Bn%2A%28n-1%29%2F2+=+36
n%2A%28n-1%29+=+72
n%5E2+-+n+-+72+=+0
Solving the above quadratic equation through factorization:
n%5E2+%2B+8%2An+-+9%2An+-+72+=+0
n%2A%28n%2B8%29+-+9%2A%28n%2B8%29+=+0
%28n-9%29%2A%28n%2B8%29+=+0
n = 9 or n = -8
Choosing the positive value of n, the number of people in the meeting = highlight%289%29
:)