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

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.