A college English instructor can teach six sections. The instructor has 5858 students enrolled in English 101, 4949 in English 102, and 6767 in English 201.

Use the Webster method to determine how many sections of each course should be offered by the instructor.

The Webster method, also known as the major fractions method, is used to apportion items (such as seats in a legislature or sections of a course) based on a set of quotas derived from proportions. Here’s how to apply the Webster method to determine the number of sections the instructor should teach for each course:

### Step 1: Calculate the total number of students
First, we add up the number of students enrolled in all the courses:
\[
\text{Total Students} = 5858 + 4949 + 6767 = 17574
\]

### Step 2: Determine the quota for each course
The quota is calculated by dividing the number of students in each course by the total number of students and then multiplying by the total number of sections (6 in this case).

For English 101:
\[
\text{Quota for English 101} = \left(\frac{5858}{17574}\right) \times 6 = \frac{35148}{17574} \approx 2.0
\]

For English 102:
\[
\text{Quota for English 102} = \left(\frac{4949}{17574}\right) \times 6 = \frac{29694}{17574} \approx 1.69
\]

For English 201:
\[
\text{Quota for English 201} = \left(\frac{6767}{17574}\right) \times 6 = \frac{40602}{17574} \approx 2.31
\]

### Step 3: Initial apportionment
Round the quotas to the nearest whole number:

- English 101: \(2.0\) rounds to \(2\) sections.
- English 102: \(1.69\) rounds to \(2\) sections.
- English 201: \(2.31\) rounds to \(2\) sections.

This gives us:
- English 101: \(2\) sections
- English 102: \(2\) sections
- English 201: \(2\) sections

However, these sections total 6, which is the number of sections available. So, this initial apportionment is correct.

### Final Result:
- **English 101:** 2 sections
- **English 102:** 2 sections
- **English 201:** 2 sections

This ensures that the sections are distributed as evenly as possible based on student enrollment using the Webster method.

Would you like more details or have any questions?

Here are some related questions:
1. What would happen if the number of sections was different?
2. How would the result change with different student enrollments?
3. What are the pros and cons of the Webster method?
4. How does the Webster method compare with the Hamilton method?
5. How can this method be applied to non-educational scenarios?

**Tip:** Always double-check your rounding decisions in apportionment methods to ensure that the total remains consistent with the available resources.

A college English instructor can teach six sections. The instructor has 5858 students enrolled in English 101, 4949 in English 102, and 6767 in English 201. Use the Webster method to determine how many sections of each course should be offered by the instructor.

Apply the Webster method to apportion 6 sections for an English instructor with 5858 students in English 101, 4949 in English 102, and 6767 in English 201. Learn how to distribute course sections based on student enrollment using a detailed step-by-step guide.

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