Let the total number of people in the cinema hall be \( x \).
According to the problem:
- The percentage of children is 22.5%, so the number of children is \( 0.225x \).
- The percentage of men is 47.5%, so the number of men is \( 0.475x \).
- The number of women is given as 84.
The total number of people can be represented as: \[ \text{Total} = \text{Children} + \text{Men} + \text{Women} \] Substituting the known values: \[ x = 0.225x + 0.475x + 84 \]
Combining the terms involving \( x \): \[ x = (0.225 + 0.475)x + 84 \] \[ x = 0.7x + 84 \]
Now, isolate \( x \) by subtracting \( 0.7x \) from both sides: \[ x - 0.7x = 84 \] \[ 0.3x = 84 \]
Now, solve for \( x \): \[ x = \frac{84}{0.3} = 280 \]
Thus, the total number of people in the cinema hall is 280.
Next, we calculate the number of men: \[ \text{Number of Men} = 0.475x = 0.475 \times 280 \]
Calculating this: \[ 0.475 \times 280 = 133 \]
Therefore, the number of men in the hall is \( \boxed{133} \).