Question

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

Answer 1

@iGreen.

Answer 2

Trick question.

66 * 2 will be the handshakes..

Answer 3

NVm

Answer 4

no 66 were the handshakes

Answer 5

Hold on a minute

Answer 6

Are you asking these for fun? Or are they part of your school?

Answer 7

do 66/2

Answer 8

actually i would say both

Answer 9

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

Answer 10

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

Answer 11

you see, my math teacher gives us a point for every homework done all together as a class.

Answer 12

when we get 10 we get a party

Answer 13

o yea i remember those..

Answer 14

he said if we get 50 in a row, he'll take us to a field trip all to ourselves wherever we want it

Answer 15

we have 49 so today he gave him this online work

Answer 16

thank you
12

In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.

Answer 17

sorry you were wrong