https://file.aiquickdraw.com/mathbot/file/17267271630456zrme8sf.jpg

Let's break down the problem step by step.

### 1. **Find the standard divisor:**
The standard divisor is calculated by dividing the total number of candies (40) by the total number of pages read by all students. The formula is:

\[
\text{Standard Divisor} = \frac{\text{Total Candies}}{\text{Total Pages Read}}
\]

First, let's sum the number of pages read by all the students:
\[
105 + 305 + 580 + 430 = 1420
\]

Now, using the formula:
\[
\text{Standard Divisor} = \frac{40}{1420}
\]

Let's calculate this.

### 2. **Find the standard quota for Yan:**
The standard quota for each student is calculated by multiplying the number of pages the student read by the standard divisor. For Yan, the formula is:

\[
\text{Standard Quota for Yan} = 105 \times \text{Standard Divisor}
\]

I'll calculate this after finding the standard divisor.

### 3. **Find the initial apportionment for Yan:**
The initial apportionment is the integer part (whole number) of the standard quota.

I'll go ahead and calculate all the needed values now.Here are the results:

1. **Standard divisor**: \(0.0282\) (rounded to 4 decimal places)
2. **Standard quota for Yan**: \(2.9577\) (rounded to 4 decimal places)
3. **Initial apportionment for Yan**: 2 (this is the integer part of the standard quota)

Let me know if you'd like further clarification or details!

---

Here are 5 related questions you could consider:
1. How would you calculate the standard quota for the other students?
2. What is the total number of candies distributed after the initial apportionment?
3. How does Hamilton's method deal with any remaining candies?
4. What is the meaning of the fractional part in the standard quota?
5. How would the distribution change if more candies were added?

**Tip**: Hamilton's method deals with remainders by distributing leftover candies to the students with the largest fractional parts.

A teacher wishes to distribute 40 identical pieces of candy among 4 students, based on how many pages of a book they read last month, using Hamilton's method. The table lists the total number of pages read by each student: Yan - 105, Ermias - 305, Katelyn - 580, Nathan - 430. Calculate the standard divisor, standard quota for Yan, and the initial apportionment for Yan.

Learn how to use Hamilton's Method to distribute 40 candies among 4 students based on the number of pages they read. Includes step-by-step calculations for finding the standard divisor, standard quota, and initial apportionment for each student.

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