We need to apportion 70 representatives among five states with the following populations: - Apprecia: 300,500 - Beauti: 200,000 - Contentia: 50,000 - Dashin: 38,000 - Enjoya: 21,500

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To apportion **70 representatives** among the five states based on their populations, we'll use a **standard divisor method** (similar to the Hamilton method) to ensure a fair distribution proportional to each state's population.

### **1. Calculate Total Population**

First, sum the populations of all states:

- **Apprecia:** 300,500
- **Beauti:** 200,000
- **Contentia:** 50,000
- **Dashin:** 38,000
- **Enjoya:** 21,500

**Total Population = 300,500 + 200,000 + 50,000 + 38,000 + 21,500 = 610,000**

### **2. Determine Population per Representative**

Divide the total population by the number of representatives to find the population each representative should represent:

$$
\text{Population per Representative} = \frac{610,000}{70} ≈ 8,714 \text{ people/representative}
$$

### **3. Initial Allocation**

Divide each state's population by the population per representative and take the integer part (floor) to allocate representatives initially:

- **Apprecia:** $$ \frac{300,500}{8,714} ≈ 34.47 $$ → **34 representatives**
- **Beauti:** $$ \frac{200,000}{8,714} ≈ 22.98 $$ → **22 representatives**
- **Contentia:** $$ \frac{50,000}{8,714} ≈ 5.73 $$ → **5 representatives**
- **Dashin:** $$ \frac{38,000}{8,714} ≈ 4.36 $$ → **4 representatives**
- **Enjoya:** $$ \frac{21,500}{8,714} ≈ 2.47 $$ → **2 representatives**

**Total Allocated Initially = 34 + 22 + 5 + 4 + 2 = 67 representatives**

### **4. Allocate Remaining Representatives**

There are **3 remaining seats** to be allocated. Assign these based on the largest fractional parts from the initial division:

- **Beauti:** 0.98
- **Contentia:** 0.73
- **Apprecia:** 0.47
- **Enjoya:** 0.47
- **Dashin:** 0.36

**Allocation Order:**

1. **Beauti** gets **1 additional representative** (highest fractional part: 0.98)
2. **Contentia** gets **1 additional representative** (next highest: 0.73)
3. **Apprecia** gets **1 additional representative** (next: 0.47)

**Final Allocation:**

- **Apprecia:** 34 + 1 = **35 representatives**
- **Beauti:** 22 + 1 = **23 representatives**
- **Contentia:** 5 + 1 = **6 representatives**
- **Dashin:** **4 representatives**
- **Enjoya:** **2 representatives**

**Total Representatives Allocated = 35 + 23 + 6 + 4 + 2 = 70 representatives**

### **Summary of Apportionment**

| **State**    | **Population** | **Representatives** |
|--------------|-----------------|---------------------|
| **Apprecia** | 300,500         | 35                  |
| **Beauti**   | 200,000         | 23                  |
| **Contentia**| 50,000          | 6                   |
| **Dashin**   | 38,000          | 4                   |
| **Enjoya**   | 21,500          | 2                   |
| **Total**    | 610,000         | 70                  |

This allocation ensures that each state receives representatives proportional to its population while adhering to the total of 70 representatives.
**Apportionment of 70 Representatives:** | **State** | **Population** | **Representatives** | |--------------|-----------------|---------------------| | **Apprecia** | 300,500 | 35 | | **Beauti** | 200,000 | 23 | | **Contentia**| 50,000 | 6 | | **Dashin** | 38,000 | 4 | | **Enjoya** | 21,500 | 2 | | **Total** | 610,000 | 70 | Each state is allocated representatives based on its population, ensuring a fair distribution of 70 representatives in total.

We need to apportion 70 representatives among five states with the following populations: - Apprecia: 300,500 - Beauti: 200,000 - Contentia: 50,000 - Dashin: 38,000 - Enjoya: 21,500

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