Question

the legislature in a state has 39 seats. apportion these seats to the five counties below using jeffersons method. county population seats received adams 428,000 grant 296,000 colton 288,000 davis 147,000 hayes 153,000 check answer

Explanation:

Step1: Calculate the total population

The total population \(P = 428000+296000 + 288000+147000+153000=1312000\)

Step2: Find the initial divisor

The initial divisor \(d=\frac{\text{Total Population}}{\text{Total Seats}}=\frac{1312000}{39}\approx33641\)

Step3: Calculate the modified quotas (by trial - and - error to adjust the divisor so that the sum of the lower - bounds is 39)

Let's try \(d = 32000\)

• For Adams: \(\frac{428000}{32000}=13.375\), lower - bound \(= 13\)
• For Grant: \(\frac{296000}{32000}=9.25\), lower - bound \(= 9\)
• For Colton: \(\frac{288000}{32000}=9\), lower - bound \(= 9\)
• For Davis: \(\frac{147000}{32000}=4.59375\), lower - bound \(= 4\)
• For Hayes: \(\frac{153000}{32000}=4.78125\), lower - bound \(= 4\)

The sum of lower - bounds \(13 + 9+9+4+4=39\)

Answer:

Adams: \(13\), Grant: \(9\), Colton: \(9\), Davis: \(4\), Hayes: \(4\)