Question

Suppose that a small country consists of four​ states:

A​ (population 1 comma 326 comma 000​),
B​ (population 1 comma 068 comma 000​),
C​ (population 524 comma 000​), and
D​ (population 82 comma 000​).

Suppose that there are 150 seats in the​ legislature, to be apportioned among the four states based on their respective populations. ​

(a) Find the standard divisor. ​

(b) Find each​ state's standard quota.

Answer 1

a.) Standard Divisor = 20000

b.) Standard Quota for State A = 66

Standard Quota for State B = 54

Standard Quota for State C = 26

Standard Quota for State D = 4

Explanation:

The country consists of four states

A B C D

1,326,000 1,068,000 524,000 82,000

Total population = 1326000 + 1068000 + 524000 + 82000

= 3000000

It is said that there are 150 seats in the legislature that have to be apportioned among the four states based on their respective states.

a.) Find the standard divisor

Standard Divisor =
`\frac{Total \hspace{0.1cm} population }{Number \hspace{0.1cm} of \hspace{0.1cm} seats} = (3000000)/(150) = 20000`

b.) Each state's standard quota.

Standard Quota for State A =
`(1326000)/(20000) = 66.3 \approx 66`

Standard Quota for State B =
`(1068000)/(20000) = 53.4 \approx 54`

Standard Quota for State C =
`(524000)/(20000) = 26.2 \approx 26`

Standard Quota for State D =
`(82000)/(20000) = 4.1 \approx 4`

If the quota are rounded to the nearest number and added then we find that the total is 149 and we so we take the quota which has the highest decimal part and round up and then summing all the quotas we get a total of 150 seats.