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

Mathematics

2 answers:

Gnoma [55]2 years ago

3 0

There would be 12 people at the party!

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.

Hope this helps!

nataly862011 [7]2 years ago

3 0

Answer:

Uhm. You didnt get this from me, But If there was 66 handshakes, and each person shakes another persons hand, all you gotta do is divide it by 2 and you get 66.

Step-by-step explanation:

Im right ik ty ;)

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