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.