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The problem in the image involves apportioning 18 tutors among four subjects (Math, English, Chemistry, and Biology) using **Webster's method of apportionment**. You are asked to determine the initial allocation and the final apportionment after rounding, using a modified divisor.

### Steps to solve using **Webster's Method**:

1. **Calculate the Standard Divisor**:  
   The standard divisor is obtained by dividing the total number of students enrolled by the total number of tutors available:
   \[
   \text{Standard Divisor} = \frac{\text{Total Students Enrolled}}{\text{Total Tutors}}
   \]
   In this case, the total students enrolled is \( 295 + 250 + 125 + 60 = 730 \), and the total tutors available is 18. Therefore,
   \[
   \text{Standard Divisor} = \frac{730}{18} \approx 40.56
   \]

2. **Initial Allocation**:
   Now, divide the number of students in each subject by the standard divisor:
   - Math: \( \frac{295}{40.56} \approx 7.27 \)
   - English: \( \frac{250}{40.56} \approx 6.16 \)
   - Chemistry: \( \frac{125}{40.56} \approx 3.08 \)
   - Biology: \( \frac{60}{40.56} \approx 1.48 \)

   Apply Webster's method, which rounds each quota to the nearest whole number:
   - Math: \( 7.27 \) rounds to 7
   - English: \( 6.16 \) rounds to 6
   - Chemistry: \( 3.08 \) rounds to 3
   - Biology: \( 1.48 \) rounds to 2

   This gives us the initial apportionment: Math 7, English 6, Chemistry 3, Biology 2.

3. **Modified Divisor**:  
   You need to adjust the divisor slightly if the total number of tutors assigned is different from 18. In this case, the modified divisor is asked as 40, but it is incorrect (probably slightly off due to rounding). Given the total number of tutors exactly matches 18, a divisor close to 40.56 should be ideal. Hence, try a modified divisor like 40.56.

### Conclusion:
The divisor should be close to the standard divisor, approximately 40.56. It seems 40 was a near estimate but not exact.

Do you have any more questions, or would you like further clarifications?

### Further Questions:
1. How does Webster’s method differ from other apportionment methods (like Hamilton’s method)?
2. Why is the standard divisor important in the apportionment process?
3. Can you explain the rounding process in Webster's method and why it works well?
4. What happens if the total number of assigned tutors doesn't match the available tutors?
5. How would the apportionment change if the number of students or tutors was different?

**Tip**: When using Webster’s method, always ensure the rounding rule is applied carefully to each subject’s allocation to get the final distribution exactly right.

A college offers tutoring in Math, English, Chemistry, and Biology. The number of students enrolled in each subject is given. The college can hire 18 tutors. Use Webster's method to determine the initial allocation and apportion the tutors across the subjects.

Learn how to apportion 18 tutors across Math, English, Chemistry, and Biology for 730 students using Webster's method. The problem includes calculating the standard divisor, initial allocation, and modified divisor for precise rounding. Suitable for advanced high school or college students.

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