Question

Suppose that a small country consists of four​ states: A​ (population 3,291,000) B​ (population 02,913,000​), C​ (population 806,000​), and D​ (population 990,000​).

Suppose that there are M= 160 seats in the​ legislature, to be apportioned among the four states based on their respective populations. Find the apportionment of each state under​ Jefferson's method.​ (Hint: Look for suitable divisors in the interval 49,250 to 49,550​.)

Complete the table of each​ state's apportionment below.

Answer 1

Given

A small country consists of four​ states

A​ population = 3,291,000

B population = 2,913,000​

C​ population = 806,000​ and

D​ population = 990,000​

Seats M =160

Total population =   3,291,000 + 2,913,000​ + 806,000 + 990,000​

= 8,000,000

standard divisor (SD) = 8,000,000 / 160

= 50,000

MQ = Total population / MD

MD = modified divisor

MD = 50,000 -160

= 49,840

State	Population	MQ	Approximated
A	3,291,000	66.03	66
B	2,913,000	58.45	58
C	806,000​	16.17	16
D	990,000	19.86	20

TOTAL = 66 + 58 + 16 + 20 = 160.

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