Victoriasushchik
  • Victoriasushchik
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Vocaloid
  • Vocaloid
use the formula x(x-1)/2 = 66 and solve for x
Victoriasushchik
  • Victoriasushchik
ohh ok so i got this: 12 In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n. Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66. This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party. Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Victoriasushchik
  • Victoriasushchik
is it right? @Vocaloid

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Vocaloid
  • Vocaloid
yeah, that's the solution is there anything you'd like me to explain or clarify?
Victoriasushchik
  • Victoriasushchik
Nope Thank-you!

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