SOLUTION: frank is at a meeting to review his selections for the committee Frank remembers clearly that everyone shook hands with everyone else and that there were exactly 105 handshakes, bu

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Question 1057486: frank is at a meeting to review his selections for the committee Frank remembers clearly that everyone shook hands with everyone else and that there were exactly 105 handshakes, but can't remember how many people were at the meeting. How many were there?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
This is a very famous and common instructional example. Look for information on it for your level. Use the vertices of regular polygons, starting with triangle, and work upward, counting the number of all diagonals and sides for each figure.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Frank is at a meeting to review his selections for the committee Frank remembers clearly that everyone shook hands
with everyone else and that there were exactly 105 handshakes, but can't remember
How many people were at the meeting. How many were there?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

If there were "n" people in the room and everyone shaked hand with everyone else, the total number of handshakes was .

So, for your problem you have this equation

 = 105.

Simplify and solve for "n":

n*(n-1) = 2*105,

n*(n-1) = 210  ---> you may guess n = 14 (or solve the quadratic equation for n.

Answere.  There were 14 persons in the meeting.

Ignore the instructions of "josgarithmetic", since they are not relevant.


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