At a party, everyone must shake the hand of the other. If the total number of handshakes is 66, there are ----people at the party.

At a party, everyone must shake the hand of the other. If the total number of handshakes is 66, there are ----people at the party. ?

Created: 1 week ago | Updated: 1 week ago | Created By:

Imran Ahmed

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Best Answer Explained in Below-:

To find the number of people at the party, we can use the following formula for calculating the total number of handshakes in a group:Total handshakes = (n * (n - 1)) / 2Where "n" is the number of people at the party.Given that there were 66 handshakes, we can set up the equation:66 = (n * (n - 1)) / 2Now, let's solve for "n." First, multiply both sides by 2 to remove the fraction:2 * 66 = n * (n - 1)132 = n^2 - nNow, rearrange the equation:n^2 - n - 132 = 0We have a quadratic equation, and we can factor it:(n - 12)(n + 11) = 0Setting each factor equal to zero:n - 12 = 0 n = 12n + 11 = 0 n = -11Since the number of people cannot be negative, we discard the negative solution.Therefore, there were 12 people at the party.The correct answer is 12.

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