To solve this problem, we can use the formula for the number of handshakes that occur in a group of people. This can be represented by the formula:
H = n(n – 1) / 2
where H is the number of handshakes and n is the number of people at the party. In this case, we know that H = 15.
Now, we can set up the equation:
15 = n(n – 1) / 2
To eliminate the fraction, we can multiply both sides by 2:
30 = n(n – 1)
This simplifies to:
n^2 – n – 30 = 0
Next, we can factor this quadratic equation:
(n – 6)(n + 5) = 0
This gives us two potential solutions for n: n = 6 or n = -5. Since the number of people cannot be negative, we take n = 6.
Thus, there were 6 people at the party.