To determine the final apportionment of the 13 legislative seats among the three states using the Hamilton method, follow these steps:
1. Calculate the Standard Quotas:
- State 1: [tex]\(2.67\)[/tex]
- State 2: [tex]\(6.92\)[/tex]
- State 3: [tex]\(4.17\)[/tex]
2. Calculate the Initial Apportionment:
Take the integer part of each standard quota:
- State 1: [tex]\( \text{floor}(2.67) = 2 \)[/tex]
- State 2: [tex]\( \text{floor}(6.92) = 6 \)[/tex]
- State 3: [tex]\( \text{floor}(4.17) = 4 \)[/tex]
Summing these initial apportionments: [tex]\(2 + 6 + 4 = 12\)[/tex] seats.
3. Determine Remaining Seats to Distribute:
The total number of seats available is 13. After the initial apportionment, 12 seats have been allocated, so there is 1 seat remaining to be distributed.
4. Distribute Remaining Seats Based on Fractional Parts:
- State 1: [tex]\(2.67 - 2 = 0.67\)[/tex]
- State 2: [tex]\(6.92 - 6 = 0.92\)[/tex]
- State 3: [tex]\(4.17 - 4 = 0.17\)[/tex]
Identify the state with the largest fractional part:
- State 2 has the largest fractional part of [tex]\(0.92\)[/tex].
Allocate the remaining seat to State 2.
5. Calculate the Final Apportionment:
Add the additional seats to the initial apportionment:
- State 1: [tex]\( 2 \)[/tex]
- State 2: [tex]\( 6 + 1 = 7 \)[/tex]
- State 3: [tex]\( 4 \)[/tex]
Thus, the final apportionment using the Hamilton method is:
[tex]\[
\boxed{(2,7,4)}
\][/tex]
So, the correct answer is:
(A) [tex]\(2, 7, 4\)[/tex]
