At a meeting, everyone shook hands with everybody else. There were 66 handshakes. How many people were in the room?
The number of handshakes would be the sum of n+1 people. Forming the following sum.
1+2+3+4+.....+n
n(n+1)/2 which would equal 66 in this question.
n(n+1)/2 = 66
1/2(n^2+n) = 66
n^2+2n-132=0
Solving this quadratic gives the solution of n =11
Therefore the number of people at the meeting would be n+1 -> 11+1=12
12 people at the meeting
The number of handshakes would be the sum of n+1 people. Forming the following sum.
1+2+3+4+.....+n
n(n+1)/2 which would equal 66 in this question.
n(n+1)/2 = 66
1/2(n^2+n) = 66
n^2+2n-132=0
Solving this quadratic gives the solution of n =11
Therefore the number of people at the meeting would be n+1 -> 11+1=12
12 people at the meeting
