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The problem you are working on requires the use of Hamilton's method of apportionment to allocate nurses across various hospital units. Here’s a breakdown of how to solve this step by step:

### Problem Information:
- There are 230 nurses to be divided among 5 units.
- The units are:
  - Emergency Care Unit (ECU) - 26 beds
  - Intensive Care Unit (ICU) - 15 beds
  - Maternity Unit (MU) - 37 beds
  - Pediatrics Unit (PU) - 27 beds
  - Surgery Unit (SU) - 25 beds

### Hamilton's Method Overview:
Hamilton’s method works by first assigning an initial number of nurses based on the standard quota and then distributing any remaining nurses based on the fractional part of the quotas. The process is as follows:

1. **Step 1: Calculate the total number of beds:**
   The total number of beds is \( 26 + 15 + 37 + 27 + 25 = 130 \).

2. **Step 2: Calculate the standard divisor:**
   The standard divisor \( D \) is the total number of beds divided by the total number of nurses:
   \[
   D = \frac{130}{230} \approx 0.5652
   \]
   This divisor helps to calculate how many nurses are apportioned per bed.

3. **Step 3: Calculate the standard quota for each unit:**
   Use the divisor to calculate the quota for each unit:
   \[
   \text{Quota for ECU} = \frac{26}{D} = \frac{26}{0.5652} \approx 46.01
   \]
   \[
   \text{Quota for ICU} = \frac{15}{D} = \frac{15}{0.5652} \approx 26.53
   \]
   \[
   \text{Quota for MU} = \frac{37}{D} = \frac{37}{0.5652} \approx 65.47
   \]
   \[
   \text{Quota for PU} = \frac{27}{D} = \frac{27}{0.5652} \approx 47.75
   \]
   \[
   \text{Quota for SU} = \frac{25}{D} = \frac{25}{0.5652} \approx 44.25
   \]

4. **Step 4: Allocate based on the integer part of the quotas:**
   Assign the integer part of each quota:
   - ECU: 46 nurses
   - ICU: 26 nurses
   - MU: 65 nurses
   - PU: 47 nurses
   - SU: 44 nurses

   This sums to \( 46 + 26 + 65 + 47 + 44 = 228 \) nurses.

5. **Step 5: Distribute the remaining 2 nurses:**
   The remaining 2 nurses are distributed to the units with the largest fractional parts of the quotas:
   - ICU: Fractional part = 0.53
   - MU: Fractional part = 0.47
   - PU: Fractional part = 0.75
   - SU: Fractional part = 0.25
   - ECU: Fractional part = 0.01

   The largest fractional parts are for PU (0.75) and ICU (0.53), so the remaining 2 nurses go to these units.

### Final Apportionment:
- ECU: 46 nurses
- ICU: 27 nurses (26 + 1)
- MU: 65 nurses
- PU: 48 nurses (47 + 1)
- SU: 44 nurses

These are the numbers of nurses to be allocated to each unit.

Would you like more detailed steps or have any specific questions on this?

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Here are 5 related questions you might find interesting:
1. How does Jefferson’s method of apportionment differ from Hamilton’s method?
2. What happens if there are more remaining nurses after the first distribution in Hamilton’s method?
3. How would the apportionment change if the total number of nurses increased to 250?
4. What are the advantages and disadvantages of using Hamilton’s method in resource allocation?
5. Can Hamilton’s method always guarantee an unbiased distribution? Why or why not?

**Tip:** Always double-check the fractional parts when distributing the remaining resources, as small differences can affect the outcome significantly.

A certain hospital has five major units: Emergency Care (ECU), Intensive Care (ICU), Maternity (MU), Pediatrics (PU), and Surgery (SU). There are 230 nurses, and they are apportioned to the units based on the number of beds in each unit. How many nurses should be assigned to each unit?

Learn how to apportion 230 nurses across five hospital units using Hamilton's method based on the number of beds in each unit. The solution covers calculating the standard divisor, determining quotas, and distributing any remaining nurses. Suitable for high school students in Grades 9-12.

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