Math Problem Statement

The table to the right shows four​ states, their 2010​ populations, and their number of seats in a particular branch of​ government, which has a total of 379 seats. For state Upper B​, find the standard quota. Use the value 310 million for the total population. Explain whether each state is relatively​ under- or overrepresented in the House. State Population Seats A 6 comma 104 comma 000 7 B 18 comma 269 comma 000 22 C 16 comma 587 comma 000 21 D 17 comma 621 comma 000 21

Question content area bottom Part 1 Select the correct choice below and fill in the answer box to complete your choice. ​(Round to two decimal places as​ needed.) A. State Upper B is overrepresented because its standard quota of    enter your response here is less than its number of​ representatives, 22. B. State Upper B is underrepresented because its standard quota of    enter your response here is more than its number of​ representatives, 22.

Solution

To determine the standard quota for state B, we need to use the following formula:

Standard Quota for State B=(Population of State BTotal Population)×Total Seats in Government\text{Standard Quota for State B} = \left( \frac{\text{Population of State B}}{\text{Total Population}} \right) \times \text{Total Seats in Government}

Given the following information:

  • Population of State B: 18,269,000
  • Total Population: 310,000,000 (310 million)
  • Total Seats: 379

Let's calculate:

Standard Quota for State B=(18,269,000310,000,000)×379\text{Standard Quota for State B} = \left( \frac{18,269,000}{310,000,000} \right) \times 379

Now, let me compute that.The standard quota for State B is approximately 22.34.

Since the actual number of seats allocated to State B is 22 and the standard quota is 22.34, State B is slightly underrepresented, because its standard quota (22.34) is higher than its number of representatives (22).

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

  1. How do we calculate the standard quota for other states?
  2. What does it mean if a state is overrepresented or underrepresented?
  3. How do changes in population affect representation in a fixed number of seats?
  4. What are rounding methods used in apportionment (e.g., Hamilton or Jefferson methods)?
  5. How would a shift in total population impact the number of seats for each state?

Tip: The concept of standard quota helps identify how closely representation reflects a state's population, ensuring fairness in a proportional system.

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Math Problem Analysis

Mathematical Concepts

Proportional Representation
Standard Quota

Formulas

Standard Quota = (Population of State / Total Population) * Total Seats

Theorems

Apportionment Theorem

Suitable Grade Level

Grades 9-12