Chapter 4, Problem 1E

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.

To determine

(a)

To find:

The standard divisor of given population.

Answer to Problem 1E

Solution:

The standard divisor for each seat of Bandana congress is $50,000$.

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,

$\text{SD}=\frac{\text{Total number of population}}{\text{Number of seats}}$

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,

$\begin{array}{rll}\text{Total number of population}& =& 3310000+2670000+1330000+690000\\ & =& 8,000,000\end{array}$$\mathrm{...}\left(1\right)$

The required standard divisor is given as,

$\text{SD}=\frac{\text{Total number of population}}{\text{Number of seats}}$

It is given that the number of seats is 160.

From equation $\left(1\right)$, substitute 8, 000, 000 for total number of population and 160 for number of seats in the above equation.

$\begin{array}{rll}\text{SD}& =& \frac{8,000,000}{160}\\ & =& 50,000\end{array}$

Conclusion:

Thus, the standard divisor for each seat of Bandana congress is $50,000$.

To determine

(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	$66.2$	$53.4$	$26.6$	$13.8$

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 ($q^N$) for any state is the ratio of their respective state population to the standard divisor, that is,

$q^N=\frac{\text{Population of Nth state}}{\text{Standard Divisor}}$

Calculation:

From part 1, the standard divisor of given population is,

$\text{SD}=50,000$$\mathrm{...}\left(1\right)$

The standard quota of state Apure is given as,

$q^1=\frac{\text{Population of the state Apure}}{\text{Standard Divisor}}$

It is given that the population of Apure is 3, 310, 000 people.

From equation $\left(1\right)$, substitute 3, 310, 000 for the population of the state Apure and $50,000$ for standard divisor in the above equation.

$\begin{array}{rll}{q}^1& =& \frac{\text{3310000}}{50000}\\ & =& 66.2\end{array}$

The standard quota of state Barinas is given as,

$q^2=\frac{\text{Population of the state Barinas}}{\text{Standard Divisor}}$

It is given that the population of Barinas is 2, 670, 000 people.

From equation $\left(1\right)$, substitute 2, 670, 000 for the population of the state Barinas and $50,000$ for standard divisor in the above equation.

$\begin{array}{rll}{q}^2& =& \frac{\text{2670000}}{50000}\\ & =& 53.4\end{array}$

The standard quota of state Carabobo is given as,

$q^3=\frac{\text{Population of the state Carabobo}}{\text{Standard Divisor}}$

It is given that the population of Carabobo is 1, 330, 000 people.

From equation $\left(1\right)$, substitute 1, 330, 000 for the population of the state Carabobo and $50,000$ for standard divisor in the above equation.

$\begin{array}{rll}{q}^3& =& \frac{\text{1330000}}{50000}\\ & =& 26.6\end{array}$

The standard quota of state Dolores is given as,

$q^4=\frac{\text{Population of the state Dolores}}{\text{Standard Divisor}}$

It is given that the population of Dolores is 690, 000 people.

From equation $\left(1\right)$, substitute 690, 000 for the population of the state Dolores and $50,000$ for standard divisor in the above equation.

$\begin{array}{rll}{q}^4& =& \frac{\text{690000}}{50000}\\ & =& 13.8\end{array}$

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	$66.2$	$53.4$	$26.6$	$13.8$