A party has 7 men and 9 women. The number of girls is 15, and this represents half of the total people at the party. How many boys are at the party?

The number of women is 9.
The number of girls is 15.

$$\text{Girls} + \text{Women} = 15 + 9 = 24$$

This means the number of girls and women is half of the total number of people at the party.

$$\text{Total People} = 2 \times (\text{Girls} + \text{Women})$$ $$\text{Total People} = 2 \times 24 = 48$$

The total number of people is the sum of men, women, boys, and girls.
Let $B$ be the number of boys.

$$\text{Total People} = \text{Men} + \text{Women} + \text{Boys} + \text{Girls}$$ $$48 = 7 + 9 + B + 15$$

$$48 = (7 + 9 + 15) + B$$ $$48 = 31 + B$$

Subtract 31 from both sides of the equation.

$$B = 48 - 31$$ $$B = 17$$

The number of boys at the party is 17.

The final answer is $\text{17}$