9.4: Exercises
- Page ID
- 31998
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Chapter 9 Homework
- A solar system consisting of five planets has a governing council of 135 members who are apportioned proportional to the populations of the planets. The population for each planet is listed in the following table.
| Planet | Ajax | Borax | Calax | Delphi | Eljix | Total |
| Population | 183,000 | 576,000 | 274,000 | 749,000 | 243,000 | 2,025,000 |
For each planet, find the standard quota, the upper quota and the lower quota. Give your answers in a table.
- A city has seven fire districts and 585 firefighters. The number of firefighters assigned to each district is proportional to the population of the district. The population for each district is given in the following table.
| District | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Total |
| Population | 23,400 | 41,800 | 36,200 | 28,800 | 34,900 | 48,500 | 16,300 | 229,900 |
For each district, find the standard quota, the upper quota and the lower quota. Give your answers in a table.
- The country named Erau has five states and a total of 200 seats available in its House of Representatives. The number of seats that each state receives is proportional to the population of that state. The populations of the states are given in the table below.
| State | 1 | 2 | 3 | 4 | 5 | Total |
| Population | 3,500,000 | 1,200,000 | 530,000 | 999,000 | 771,000 | 7,000,000 |
For each state, find the standard quota, the upper quota and the lower quota. Give your answers in a table.
- Use Hamilton’s method to apportion the 585 firefighters in problem #2.
- Use Hamilton’s method to apportion the 135 council members in problem #1.
- Use Hamilton’s method to apportion the 200 seats in the House of Representatives in problem #3.
- A small country is made up of three separate islands: Eno, with a population of 100,300, Owt, with a population of 9,405, and Eerht with a population of 90,295. The country has a senate with 200 members whose seats are apportioned proportional to the population of each island.
- Use Hamilton’s method to apportion the 200 seats.
- The senate decides to add another seat so that they have an odd number of senators. Use Hamilton’s method to apportion the 201 seats.
- Compare your results from parts (a) and (b). This is an example of which paradox?
- Use Jefferson’s method to apportion the 585 firefighters in problem #2.
- Use Jefferson’s method to apportion the 135 council members in problem #1.
- Use Jefferson’s method to apportion the 200 seats in the House of Representatives in problem #3.
- Use Adams’s method to apportion the 135 council members in problem #1.
- Use Adams’s method to apportion the 585 firefighters in problem #2.
- Use Adam’s method to apportion the 200 seats in the House of Representatives in problem #3.
- Use Webster’s method to apportion the 585 firefighters in problem #2.
- Use Webster’s method to apportion the 135 council members in problem #1.
- Use Webster’s method to apportion the 200 seats in the House of Representatives in problem #3.
- Use Huntington-Hill’s method to apportion the 135 council members in problem #1.
- Use Huntington-Hill’s method to apportion the 585 firefighters in problem #2.
- Use Huntington-Hill’s method to apportion the 200 seats in the House of Representatives in problem #3.
- Last year a city had three school districts: North, with a population of 5,200 children, South, with a population of 10,600 children, and West, with a population of 15,100.
- Use Hamilton’s method to apportion 50 speech therapists among the districts using the populations for last year.
- This year, the city took over another school district. The new East district has a population of 9,500 children. If the number of speech therapists is increased by 15 to accommodate the new district, use Hamilton’s method to apportion the 65 speech therapists.
- Compare your results to parts (a) and (b). This is an example of which paradox?
- After the census in 1950, planet Ajax had a standard quota of 11.87 but was awarded 13 seats using Jefferson’s method. Why were people on the other planets upset about this? What rule was violated?
- Five co-workers work together on a large design project. As a reward for their effort, their boss wishes to split 50 gift cards of equal value among the employees based on the amount of time spend on the project. The time, in hours, worked by each employee is listed in the following table.
| Employee | Jack | Kim | Lisa | Mark | Nancy | Total |
| Time | 150 | 173 | 78 | 295 | 204 | 900 |
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- Use Hamilton’s method to apportion the 50 gift cards among the employees.
- At the last minute, the boss made a minor change to the design. It took Kim 8 more hours and Mark one more hour to incorporate the change. Use Hamilton’s method to apportion the 50 gift cards using the new total times for Kim (181) and Mark (296).
- Compare your answers to parts (a) and (b). Which one of the paradoxes occurred? Explain your answer.