Math Help - arithmetic problem

1. arithmetic problem

At a party , each person shakes hands with every other person . the total number of hand shakes was 66. how many persons are present at the party ?

A 6 b 11 c 12 d 18 e 33

2. Originally Posted by sri340
At a party , each person shakes hands with every other person . the total number of hand shakes was 66. how many persons are present at the party ?

A 6 b 11 c 12 d 18 e 33
Line up half of the people with the other half of the people facing them.

One line has $\frac{x}{2}$ people, so $\frac{x}{2}$ handshakes can take place.

Each person can shake hands with (x-1) other people,

hence there are $(x-1)\frac{x}{2}$ handshakes possible

$(x-1)\frac{x}{2}=66$

$(x-1)x=132$

the factors of 132 that differ by 1 are 11 and 12, hence x=12, x-1=11.

12 people are at the party.