Questions: A small country is comprised of four states, A, B, C, and D. The population of each state, in thousands, is given in the following table.
State A B C D Total
Population (in thousands) 111 240 513 636 1500
According to the country's constitution, the congress will have 60 seats, divided among the four states according to their respective populations.
a) Find the standard divisor, in thousands. How many people are there for each seat in congress?
standard divisor:
number of people for each seat:
(Type an integer in each box)
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3) - Fall 2024
Do Hormwerk - 13.3 Apportionmant Methods
Josh Marinich
.3 Apportionment Methods
Question 1, 13.3.1
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A small country is comprised of four states, A, B, C, and D. The population of each state, in thousands, is given in the following table.
\begin{tabular}{|l|c|c|c|c|c|}
\hline State & A & B & C & D & Total \\
\hline Population (in thousands) & 111 & 240 & 513 & 636 & 1500 \\
\hline
\end{tabular}
According to the country's constitution, the congress will have 60 seats, divided among the four states according to their respective populations.
a) Find the standard divisor, in thousands. How many people are there for each seat in congress?
standard divisor: $\square$
number of people for each seat: $\square$ $\square$
(Type an integer in each box)
Solution
Solution Steps
Step 1: Calculate the Standard Divisor
The standard divisor (SD) is calculated by dividing the total population (P) by the total number of seats (M).
SD = P / M = 1500 / 60 = 25
Step 2: Determine the Standard Quota for Each State
The standard quota (SQ) for each state is determined by dividing the population of that state (Pi) by the standard divisor (SD).
SQ_1 = P_1 / SD = 111 / 25 = 4
SQ_2 = P_2 / SD = 240 / 25 = 10
SQ_3 = P_3 / SD = 513 / 25 = 21
SQ_4 = P_4 / SD = 636 / 25 = 25
Step 3: Round the Standard Quotas
The standard quotas are then rounded to whole numbers. This step is simplified for demonstration.
Rounded SQ_1 = 4
Rounded SQ_2 = 10
Rounded SQ_3 = 21
Rounded SQ_4 = 25
Total seats allocated after rounding: 60
Final Answer:
State 1 is allocated 4 seats.
State 2 is allocated 10 seats.
State 3 is allocated 21 seats.
State 4 is allocated 25 seats.