There are a total of 200 students in a class who play either badminton or tennis or both. The number of boys playing only tennis is 1/3 of the total number of girls playing only one game. The number of girls playing badminton equals the number of boys in the class. The number of girls playing both games is 40\% more than the number of boys playing only badminton, and the number of girls playing only tennis is twice the number of boys playing only badminton. The number of boys playing both games is half the number of girls playing only badminton.

Compare the following quantities:

- Quantity I: Number of boys playing tennis
- Quantity II: Number of girls playing only tennis
- Quantity III: Difference between the number of boys playing only badminton and the number of students playing both games together

Which of the following is true?

Question

There are a total of 200 students in a class who play either badminton or tennis or both. The number of boys playing only tennis is 1/3 of the total number of girls playing only one game. The number of girls playing badminton equals the number of boys in the class. The number of girls playing both games is 40\% more than the number of boys playing only badminton, and the number of girls playing only tennis is twice the number of boys playing only badminton. The number of boys playing both games is half the number of girls playing only badminton.

Compare the following quantities:

- Quantity I: Number of boys playing tennis
- Quantity II: Number of girls playing only tennis
- Quantity III: Difference between the number of boys playing only badminton and the number of students playing both games together

Which of the following is true?

Accepted Answer

**Solution:**

1. Let the number of boys be $ B $ and girls be $ G $. Total students = 200, so $ B + G = 200 $.

2. Let the number of boys playing only badminton be $ x $.

3. Number of girls playing only one game = girls playing only badminton + girls playing only tennis.

4. Boys playing only tennis = $ \frac{1}{3} $ of girls playing only one game.

5. Girls playing badminton = number of boys in the class $ = B $.

6. Girls playing both games = 40\% more than boys playing only badminton = $ x + 0.4x = 1.4x $.

7. Girls playing only tennis = twice the number of boys playing only badminton = $ 2x $.

8. Boys playing both games = half the number of girls playing only badminton = $ \frac{1}{2} \times \text{girls playing only badminton} $.

9. Using these relations and the total of 200 students, solve for $ x $, $ B $, and $ G $.

10. After calculations, we find:
   - Boys playing tennis (only tennis + both) = 50
   - Girls playing only tennis = 50
   - Difference between boys playing only badminton and total playing both games = 30

Thus, Quantity I = Quantity II = 50, and Quantity III = 30.

**Answer:** Quantity I = Quantity II > Quantity III

Answer

Answer

Answer

Answer