Apportioning Congressional Seats Among States Using Population Data

Math Problem Statement

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) 130 283 571 816 1800

According to the country's constitution, the congress will have 90 seats, divided among the four states according to their respective populations. Question content area bottom Part 1 a) Find the standard divisor, in thousands. How many people are there for each seat in congress? standard divisor: 20 number of people for each seat: 20000 (Type an integer in each box.) Part 2 b) Find each state's standard quota. (Two of them have been done for you.) State A B C D Total Population (in thousands) 130 283 571 816 1800 Standard quota 6.5 enter your response here enter your response here 40.8 (Type an integer or a decimal rounded to two decimal places, if necessary, in each box.)

Solution

To solve this problem, we need to calculate the standard quota for each state. The standard quota is found by dividing the population of each state by the standard divisor, which you've already calculated as 20 (in thousands). This means that each seat in congress represents 20,000 people.

Let's calculate the standard quota for each state:

State A:
- Population = 130 (in thousands)
- Standard Quota = $\frac{130}{20} = 6.5$
State B:
- Population = 283 (in thousands)
- Standard Quota = $\frac{283}{20} = 14.15$
State C:
- Population = 571 (in thousands)
- Standard Quota = $\frac{571}{20} = 28.55$
State D:
- Population = 816 (in thousands)
- Standard Quota = $\frac{816}{20} = 40.8$

So, the standard quotas for each state are:

State A: 6.5
State B: 14.15
State C: 28.55
State D: 40.8

These quotas represent the number of seats each state should ideally receive based on their population relative to the total population.

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Math Problem Analysis

Mathematical Concepts

Proportional Allocation
Division
Rounding

Formulas

Standard Divisor = Total Population / Number of Seats
Standard Quota = State Population / Standard Divisor

Theorems

Quota Method of Apportionment

Suitable Grade Level

Grades 9-12

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