1. **State the problem:** We need to find the number of senators apportioned to State 1 (Alpha) using the Jefferson Method, given the populations of six states and a total of 30 senate seats. 2. **Formula and rules:** The Jefferson Method apportions seats by dividing each state's population by a common divisor, then rounding down (floor) the results. The divisor is adjusted until the total seats allocated equals the total number of seats (30). 3. **Given data:** - Populations: Alpha = 20000, Beta = 52000, Gamma = 30000, Delta = 18000, Epsilon = 65000, Zeta = 45000 - Total population = 230000 - Total seats = 30 4. **Initial divisor:** Calculate the initial divisor as total population divided by total seats: $$\text{divisor} = \frac{230000}{30} = 7666.67$$ 5. **Calculate initial quotas:** Divide each population by divisor and take floor: - Alpha: $\left\lfloor \frac{20000}{7666.67} \right\rfloor = \left\lfloor 2.61 \right\rfloor = 2$ - Beta: $\left\lfloor \frac{52000}{7666.67} \right\rfloor = \left\lfloor 6.78 \right\rfloor = 6$ - Gamma: $\left\lfloor \frac{30000}{7666.67} \right\rfloor = \left\lfloor 3.91 \right\rfloor = 3$ - Delta: $\left\lfloor \frac{18000}{7666.67} \right\rfloor = \left\lfloor 2.35 \right\rfloor = 2$ - Epsilon: $\left\lfloor \frac{65000}{7666.67} \right\rfloor = \left\lfloor 8.48 \right\rfloor = 8$ - Zeta: $\left\lfloor \frac{45000}{7666.67} \right\rfloor = \left\lfloor 5.87 \right\rfloor = 5$ 6. **Sum seats:** $2 + 6 + 3 + 2 + 8 + 5 = 26$ seats, which is less than 30. We need to decrease the divisor to increase seats. 7. **Adjust divisor:** Try divisor = 7000 - Alpha: $\left\lfloor \frac{20000}{7000} \right\rfloor = 2$ - Beta: $\left\lfloor \frac{52000}{7000} \right\rfloor = 7$ - Gamma: $\left\lfloor \frac{30000}{7000} \right\rfloor = 4$ - Delta: $\left\lfloor \frac{18000}{7000} \right\rfloor = 2$ - Epsilon: $\left\lfloor \frac{65000}{7000} \right\rfloor = 9$ - Zeta: $\left\lfloor \frac{45000}{7000} \right\rfloor = 6$ Sum seats: $2 + 7 + 4 + 2 + 9 + 6 = 30$ seats, which matches the total. 8. **Final apportionment for State 1 (Alpha):** 2 seats. **Answer:** 2