Explanation Given information: Total number of seats is 13 and the population of four states is as follows: State: A B C Population: 90 , 000 124 , 800 226 , 000 Revised population: 98 , 000 144 , 900 247 , 100 . All these populations are in thousands. First apportion the number of seats to three states using the given population. Total population of three states is 90 , 000 + 124 , 800 + 226 , 000 = 440 , 800 thousand. Total number of seats is 13 . Therefore, standard divisor d = 440 , 800 13 = 33907.6923 Now, divide the population of each state by the standard divisor ( d = 33907.6923 ) to get the standard quota ( q ) for each state. Then, round the standard quotas down to the nearest integer, but each state gets at least one seat Therefore, the number of seats assigned to each state is as follows: States Population Standard Quota, q Lower Quota A 90 , 000 90 , 000 33907.6923 = 2.6543 2 B 124 , 800 124 , 800 33907.6923 = 3.6806 3 C 226 , 000 226 , 000 33907.6923 = 6.6652 6 Total 11 Here, total number of seats is 13 and the total of the lower quota is 11 , that is two seats do not assign to any state. According to the Hamilton’s plan, give any additional seats, one at a time to the states with the largest fractional parts of their standard quotas. Since, the fraction part of states B and C are larger than any other states, one seat is assigned to each state. Therefore, the number of seats assigned for each state according to the Hamilton’s plan is as follows: States Population Lower Quota Hamilton's Plan A 90 , 000 2 2 B 124 , 800 3 4 C 226 , 000 6 7 Total 11 13 Now, apportion the number of seats to three states using revised population. Total revised population of the three states is 98 , 000 + 144 , 900 + 247 , 100 = 490 , 000 thousand. Total number of seats is 13 . Therefore, e standard divisor d = 490 , 000 13 = 37692.3077 Now, divide the population of each state by the standard divisor ( d = 37692

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Chapter 17.4, Problem 20PS

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Whether the population paradox occurs using Hamilton’s plan for the following apportionment.

State:ABCPopulation:90,000124,800226,000Revised population:98,000144,900247,100

Total number of seats is 13.

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Chapter 17.4, Problem 19PS

Chapter 17.4, Problem 21PS

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EBK NATURE OF MATHEMATICS

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Whether the population paradox occurs using Hamilton’s plan for the following apportionment. State: A B C Population: 90 , 000 124 , 800 226 , 000 Revised population: 98 , 000 144 , 900 247 , 100 Total number of seats is 13 .

Solution Summary: The author explains how to determine whether the population paradox occurs using Hamilton's plan for the following apportionment.

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Whether the population paradox occurs using Hamilton’s plan for the following apportionment.

State:ABCPopulation:90,000124,800226,000Revised population:98,000144,900247,100

Total number of seats is 13.

Want to see the full answer?

Chapter 17 Solutions

Whether the population paradox occurs using Hamilton’s plan for the following apportionment. State: A B C Population: 90 , 000 124 , 800 226 , 000 Revised population: 98 , 000 144 , 900 247 , 100 Total number of seats is 13 .

Solution Summary: The author explains how to determine whether the population paradox occurs using Hamilton's plan for the following apportionment.

Videos

Whether the population paradox occurs using Hamilton’s plan for the following apportionment. State:ABCPopulation:90,000124,800226,000Revised population:98,000144,900247,100 Total number of seats is 13.

Want to see the full answer?

Chapter 17 Solutions

Whether the population paradox occurs using Hamilton’s plan for the following apportionment.

State:ABCPopulation:90,000124,800226,000Revised population:98,000144,900247,100

Total number of seats is 13.