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To solve this problem, we need to determine the number of children represented in the pie chart. Here's the breakdown:

1. **Total Angle of the Pie Chart**: A full circle in a pie chart represents 360 degrees.

2. **Angles Given for Men and Women**:
   - The angle for men is 75°.
   - The angle for women is 25°.
   - Therefore, the total angle representing adults (men and women) is \(75° + 25° = 100°\).

3. **Angle Representing Children**:
   - Since the entire pie chart is 360°, the angle for children would be:
     \[
     360° - 100° = 260°
     \]

4. **Finding the Ratio of Men to Women to Children**:
   - The ratios of men, women, and children based on the angles are:
     - Men: 75°
     - Women: 25°
     - Children: 260°

5. **Calculating the Number of Men and Women**:
   - The ratio of men to women is \(75 : 25 = 3 : 1\). This means there are three times as many men as women.
   - Given that there are 350 more men than women, we can let the number of women be \(x\). Then, the number of men will be \(x + 350\).

   - From the ratio, \( \frac{x + 350}{x} = 3 \), solving for \(x\):
     \[
     x + 350 = 3x
     \]
     \[
     350 = 2x
     \]
     \[
     x = 175
     \]
   - So, the number of women is 175, and the number of men is \(175 + 350 = 525\).

6. **Calculating the Total Number of People**:
   - The number of adults (men and women) is \(525 + 175 = 700\).

7. **Finding the Number of Children**:
   - The angle for children is 260°, while the total angle for adults is 100°.
   - Therefore, the ratio of children to adults is \( \frac{260}{100} = 2.6\).

   - Since the number of adults is 700, the number of children would be:
     \[
     2.6 \times 700 = 1820
     \]

Thus, the number of children is 1,820.

Would you like more details on any step?

### Related Questions:
1. How would the solution change if there were 500 more men than women?
2. What if the pie chart also included a category for senior citizens?
3. How can we calculate percentages from the given angles?
4. How do ratios help in solving problems involving pie charts?
5. What are some real-life applications of interpreting pie charts?

### Tip:
When working with ratios, converting them into fractions or percentages can make calculations easier to understand and solve.

The pie chart shows information about people at a zoo. There were 350 more men than women. Work out the number of children.

Solve a pie chart problem where there are 350 more men than women at a zoo. Learn how to calculate the number of children by using ratios, algebra, and angles in pie charts. Suitable for students in Grades 7-9.

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