
Concept explainers
The Bandana Republic is a small country consisting of four states: Apure (population 3,310,000), Barinas (population 2,670,000), Carabobo (population 1,330,000), and Dolores (population 690,000). Suppose that there are M = 160 seats in the Bandana Congress, to be apportioned among the four states based on their respective populations.
a. Find the standard divisor.
b. Find each state’s standard quota.

(a)
To find:
The standard divisor of given population.
Answer to Problem 1E
Solution:
The standard divisor for each seat of Bandana congress is
Explanation of Solution
Given:
It is given that the four states of country Bandana Republic has respective population as, Apure of 3, 310, 000 people, Barinas of 2, 670, 000 people, Carabobo of 1, 330, 000 people and Dolores of 690, 000 people. The number of seats for Bandana congress is 160 to be apportioned from four states.
The standard divisor (SD) states the number of population per unit seat, or it can be calculated as the ratio of the total population to the number of seats allocated of the congress, that is,
Calculation:
From the given information the total population is the addition of 3, 310, 000, 2, 670, 000, 1, 330, 000 and 690, 000 people, that is,
The required standard divisor is given as,
It is given that the number of seats is 160.
From equation
Conclusion:
Thus, the standard divisor for each seat of Bandana congress is

(b)
To find:
The standard quota of each state.
Answer to Problem 1E
Solution:
Conclusion:
Thus the standard quota for respective state is,
States | Apure | Barinas | Carabobo | Dolores |
Population | 3, 310, 000 | 2, 670, 000 | 1, 330, 000 | 690, 000 |
Standard quota |
Explanation of Solution
Given:
It is given that the four states of country Bandana Republic has respective population as, Apure of 3, 310, 000 people, Barinas of 2, 670, 000 people, Carabobo of 1, 330, 000 people and Dolores of 690, 000 people. The number of seats for Bandana congress is 160 to be apportioned from four states.
The standard quotas (
Calculation:
From part 1, the standard divisor of given population is,
The standard quota of state Apure is given as,
It is given that the population of Apure is 3, 310, 000 people.
From equation
The standard quota of state Barinas is given as,
It is given that the population of Barinas is 2, 670, 000 people.
From equation
The standard quota of state Carabobo is given as,
It is given that the population of Carabobo is 1, 330, 000 people.
From equation
The standard quota of state Dolores is given as,
It is given that the population of Dolores is 690, 000 people.
From equation
Conclusion:
Thus the standard quota for respective state is,
States | Apure | Barinas | Carabobo | Dolores |
Population | 3, 310, 000 | 2, 670, 000 | 1, 330, 000 | 690, 000 |
Standard quota |
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