At a party , everyone shook hands with everybody else . There were 91…
2024
At a party , everyone shook hands with everybody else . There were 91 handshakes . How many people were at the party ?
- A.
11
- B.
13
- C.
14
- D.
15
Attempted by 24 students.
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Correct answer: C
Answer: 14
Let n be the number of people at the party. Each pair of people shakes hands once, so the total number of handshakes is given by n(n-1)/2.
Set up the equation and solve:
n(n-1)/2 = 91. Multiply both sides by 2: n(n-1) = 182, which gives n^2 - n - 182 = 0.
Factor the quadratic: (n - 14)(n + 13) = 0.
The solutions are n = 14 and n = -13. Discard the negative solution, so n = 14.
Check: 14 × 13 / 2 = 91, so there were 14 people at the party.