Question

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? Please Help, Thanks.

Answer 1

for handshaking , if n people were there then total handshakes= n(n-1)

Answer 2

Total number of people = (n-1)+(n-2)+(n-3)+(n-4)+...0
= (n-1)*(n-1+1)/2 = (n-1)*n/2 = 66
= n^2 -n = 132
=(n-12)(n+11) = 0;
= n = 12
therefore 12 people

Answer 3

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Answer 4

did you get it how to do it?

Answer 5

Yes! I just need to look over the steps a few minutes and I'll get it(: I just needed like a base on how to get the answer(: Thanks.

Answer 6

"Suppose there were 'n' people.
Then each shook hands with (n-1) people.
So total number of handshakes = n(n-1)/2
[Why divided by 2? The answer is whether person A shakes hand with person B or person B shakes hand with person A is immaterial as these two situations refer to a single handshake.]
Given total no. of handshakes = 66
So n(n-1)/2 = 66
or n^2-n = 66*2 = 132
or n^2-n-132 = 0
or n^2-12n+11n-132 = 0
or n(n-12)+11(n-12) = 0
or (n-12)(n+11) = 0
Therefore either n = 12 or n = -11.
But n being no. of people cannot be negative so n = 12 "


" https://in.answers.yahoo.com/question/index?qid=1006060200769 "

Answer 7

@no.name I thought we are not allowed to post answers from yahoo.

Answer 8

Welcome to Openstudy

Answer 9

@AntiNode I mentioned the link

Answer 10

And if it is correct why not post

Answer 11

@DivergentLover welcome.

Answer 12

@No.name oh ok...

Answer 13

Give me a reason , i checked the answer twice before posting

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Answer 16

It was on the openstudyfeedback last time