Answered

Thirteen legislative seats are being apportioned among 3 states, resulting in the standard quotas shown in the following table:

| State | Quota |
|--------|-------|
| State 1| 2.67 |
| State 2| 6.92 |
| State 3| 4.17 |

Using the Hamilton method, what is the final apportionment?

A. 2, 7, 4
B. 3, 7, 4
C. 2, 6, 4
D. 3, 6, 4



Answer :

GinnyAnswer
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]

Other Questions