To solve the problem of finding the number of men in the cinema hall, we need to break down the information given and use some basic percentage calculations. Let's go through the steps in detail. ### Step 1: Understand the Percentages We know the following: - 22.5% of the people in the cinema hall are children. - 47.5% of the people are men. - The remaining percentage will be women. ### Step 2: Calculate the Percentage of Women To find the percentage of women, we can add the percentages of children and men and subtract from 100%: \[ \text{Percentage of women} = 100\% - (22.5\% + 47.5\%) = 100\% - 70\% = 30\% \] ### Step 3: Set Up the Equation Let \( x \) be the total number of people in the cinema hall. According to the problem, we know that: - The number of women is given as 84. - Since women make up 30% of the total, we can express this as: \[ 0.30x = 84 \] ### Step 4: Solve for \( x \) To find \( x \), we can rearrange the equation: \[ x = \frac{84}{0.30} \] Calculating this gives: \[ x = 280 \] So, the total number of people in the cinema hall is 280. ### Step 5: Calculate the Number of Men Now that we have the total number of people, we can find the number of men. Since men make up 47.5% of the total, we can calculate the number of men as follows: \[ \text{Number of men} = 0.475 \times 280 \] Calculating this gives: \[ \text{Number of men} = 133 \] ### Conclusion Thus, the number of men in the cinema hall is **133**. ### Explanation of Other Options - **Option A (63)**: This is too low and does not account for the percentage of men correctly. - **Option B (84)**: This is the number of women, not men. - **Option C (113)**: This is also incorrect as it does not reflect the correct percentage of men based on the total population calculated. ### Revision Summary - To find the total number of people, use the percentages given and set up an equation based on the known quantities. - Always check the percentages to ensure they add up to 100%. - Use the total number to find specific groups (like men) by applying their respective percentages. - Double-check calculations to avoid common pitfalls in percentage conversions. The correct answer is **D. 133**.