1. **State the problem:** We need to find the number of senators apportioned to State 1 (Alpha) using the Webster Method, given the populations of six states and a total of 30 senate seats. 2. **Formula and rules:** The Webster Method assigns seats by rounding the quotas to the nearest whole number. - Calculate the standard divisor: $$\text{Standard Divisor} = \frac{\text{Total Population}}{\text{Total Seats}} = \frac{230000}{30} = 7666.67$$ - Calculate each state's quota: $$\text{Quota}_i = \frac{\text{Population}_i}{\text{Standard Divisor}}$$ - Round each quota to the nearest whole number. - If the total seats assigned do not sum to 30, adjust the divisor and repeat until the total seats equal 30. 3. **Calculate quotas:** $$\text{Quota}_1 = \frac{20000}{7666.67} \approx 2.61$$ $$\text{Quota}_2 = \frac{52000}{7666.67} \approx 6.78$$ $$\text{Quota}_3 = \frac{30000}{7666.67} \approx 3.91$$ $$\text{Quota}_4 = \frac{18000}{7666.67} \approx 2.35$$ $$\text{Quota}_5 = \frac{65000}{7666.67} \approx 8.48$$ $$\text{Quota}_6 = \frac{45000}{7666.67} \approx 5.87$$ 4. **Round quotas:** $$2.61 \to 3$$ $$6.78 \to 7$$ $$3.91 \to 4$$ $$2.35 \to 2$$ $$8.48 \to 8$$ $$5.87 \to 6$$ Sum of rounded seats: $$3 + 7 + 4 + 2 + 8 + 6 = 30$$ 5. **Since the sum is exactly 30, the apportionment is valid.** 6. **Final answer:** The number of senators apportioned to State 1 (Alpha) is **3**.