Question:

Show your work and everyone shoke hands once?

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there are a certain amount of people at a meeting. @ the meeting there was 28 hand shakes exchanged how many people were at the meeting?

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  1. so everyone shakes hands one and there are 28 handshakes.  That means there are 56 people there.  Everyone has to shake once with one other person, and that one handshake take 2 people, so you do 28 x 2.


  2. 14

    14x2=28

  3. 1, 0 handshakes.

    2, 1 handshake.

    3, 3 handshakes.

    4, 6 handshakes.

    5, 10 handshakes.

    there is a pattern. 0+1+2+3+4. use this pattern to find it out.

    6, 15 handshakes.

    7, 21 handshakes.

    8, 28 handshakes.

    there were 8 people. this is a common algebra 1 question.

  4. the handshake problem is famous

    the general solution for the # of handshakes for n people = n(n-1)/2

    so 28 = n(n-1)/2

    so 56 =  n(n-1)

    56 = n^2 -1n

    0= n^2 -1n-56

    0=(n-8)(n+7)

    by the zero property either n-8=0 or n+7=0

    so n=+8 or n=-7 but u cant have -7 people so

    n=8

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