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

 Mar 10, 2019
 #1
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To see this, imagine that  just 4 people were at the party

 

The first person shakes 3 hands

The second person shakes 2 hands

The third person shakes 1 hand

The last person has already shaken hands with everybody

 

So...the number of handshakes between 4 people =  (4)(3) / 2 =  6

 

So....it appears that the number of handshakes between n people  is just n(n - 1) /2

 

So.....we can solve this

 

n(n - 1) / 2 = 66      multiply both sides by 2

 

n(n - 1) = 132   simplify

 

n^2 - n = 132

 

n^2 - n - 132 = 0     factor

 

(n - 12)  ( n + 11) = 0

 

Setting each factor to 0  ans solving for n  ives n = -11  (reject)   or n = 12 (accept)

 

So....there wqere 12 people

 

 

cool cool cool

 Mar 10, 2019

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