Use the Hamilton method of Apportionment to make the assignment.
In a recent census, Iowa's population in thousands was 4,503, Illinois' was 8,220, and Indiana's was 5,300.
Allocate 31 members of the U.S. House of representatives to these three states.
Possible Answers:
Iowa: 11; Illinois: 12; Indiana: 8
Iowa: 9; Illinois: 14; Indiana: 8
Iowa: 8; Illinois: 14; Indiana: 9
Iowa: 7; Illinois: 16; Indiana: 8
Would the answer be C?
Thanks
To solve this problem using the Hamilton method of apportionment, we need to follow these steps:
Step 1: Calculate each state's standard divisor (SD). The standard divisor is obtained by dividing the total population by the number of seats to be allocated. In this case, the total population is the sum of the populations of Iowa, Illinois, and Indiana (4,503 + 8,220 + 5,300 = 18,023), and the number of seats to be allocated is 31. Therefore, SD = 18,023 / 31 = 581.38 (rounded to two decimal places).
Step 2: Calculate the lower quotas (LQ) for each state. The lower quota represents the exact number of seats that each state is entitled to, without considering any remaining decimal portions. The lower quota is obtained by dividing each state's population by the standard divisor and rounding down to the nearest whole number.
For Iowa: LQ = 4,503 / 581.38 = 7.74 ≈ 7
For Illinois: LQ = 8,220 / 581.38 = 14.15 ≈ 14
For Indiana: LQ = 5,300 / 581.38 = 9.12 ≈ 9
Step 3: Calculate the adjusted quotas (AQ) for each state. The adjusted quotas represent the hypothetical number of seats each state would be allocated if decimal portions were considered. The adjusted quota is obtained by dividing the state's population by the standard divisor and rounding to one decimal place.
For Iowa: AQ = 4,503 / 581.38 = 7.74
For Illinois: AQ = 8,220 / 581.38 = 14.15
For Indiana: AQ = 5,300 / 581.38 = 9.12
Step 4: Calculate the priority values (PV) for each state. The priority value represents the decimal portion of the adjusted quota. It is obtained by subtracting the rounded lower quota from the adjusted quota.
For Iowa: PV = 7.74 - 7 = 0.74
For Illinois: PV = 14.15 - 14 = 0.15
For Indiana: PV = 9.12 - 9 = 0.12
Step 5: Determine the initial seat assignments for each state. For each state, compare the priority values and assign one seat to the state with the highest priority value. Repeat this process until the total number of allocated seats reaches the desired number of seats (31 in this case).
In this case, Iowa has the highest priority value (0.74), so Iowa is assigned a seat.
After the first seat is assigned, update the adjusted quota and priority values for the remaining states.
For Illinois: AQ = 14.15 - 1 = 13.15, PV = 0.15
For Indiana: AQ = 9.12 - 1 = 8.12, PV = 0.12
Now, Illinois has the highest priority value (0.15), so Illinois is assigned a seat.
Update the adjusted quota and priority value for Indiana.
For Indiana: AQ = 8.12 - 1 = 7.12, PV = 0.12
Indiana has the highest priority value (0.12) among the remaining states, so Indiana is assigned a seat.
Step 6: Repeat Step 5 until all seats are allocated. In this case, we can see that Illinois has the highest priority value at each step, so Illinois continues to be assigned seats until all 31 seats are allocated.
Final seat assignments:
Iowa: 8
Illinois: 14
Indiana: 9
Therefore, the correct answer is Iowa: 8, Illinois: 14, Indiana: 9, which matches option C.