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

Question

vocaloid · Answer

use the formula

x(x-1)/2 = 66

and solve for x

victoriasushchik · Answer

ohh ok so i got this:
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.

victoriasushchik · Answer

is it right?      @Vocaloid

vocaloid · Answer

yeah, that's the solution 

is there anything you'd like me to explain or clarify?

victoriasushchik · Answer

Nope Thank-you!