Explanation The city district attorney has 60 litigators to be divided among three courts, and the numbers of pending cases for each court are as follows: Court: A B C Total Pending cases: 209 769 2, 022 3, 000 . The total number of pending cases of three courts is 3 , 000 . The total number of litigators is 60 . Therefore, the standard divisor d = 3000 60 = 50 . Now divide the number of pending cases of each court by the standard divisor ( d = 50 ) to get the standard quota ( q ) for each court. Then round the standard quotas down to the nearest integer, but each court gets at least one litigator. Therefore, the number of litigators assigned to each court is as follows: Court Pending cases Standard Quota, q Lower Quota A 209 209 50 = 4 .18 4 B 769 769 50 = 15.38 15 C 2, 022 2022 50 = 40.44 40 Total 3, 000 59 Here the total numbers of litigators are 60 , and the total of the lower quotas is 59 , that is one litigator does not assign to any court. According to Hamilton’s plan, give any additional seats, one at a time to the states with the largest fractional parts of their standard quotas. Since fraction part of the court C is larger than any other courts, one litigator is assigned to the court C . Therefore, the number of litigators assigned for each court according to Hamilton’s plan is as follows: Court Pending cases Lower Quota Hamilton's Plan A 209 4 4 B 769 15 15 C 2, 022 40 40 + 1 = 41 Total 3, 000 59 60 Now increase the number of litigators by 5 , that is, increased from 60 to 65 for the new court D , so the total number of litigators becomes 65 for the four courts as below: Court: A B C D Total Pending cases: 209 769 2, 022 260 3 , 260

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 17.4, Problem 32PS

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Whether the New states paradox occurs when 5 new litigators are added for the new court.

Court: A B CTotalPending cases:2097692, 0223, 000

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Chapter 17.4, Problem 31PS

Chapter 17.4, Problem 33PS

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Nature of Mathematics (MindTap Course List)

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Whether the New states paradox occurs when 5 new litigators are added for the new court. Court: A B C Total Pending cases: 209 769 2, 022 3, 000

Solution Summary: The author explains that the New states paradox occurs when 5 new litigators are added for the new court.

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Whether the New states paradox occurs when 5 new litigators are added for the new court.

Court: A B CTotalPending cases:2097692, 0223, 000

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Whether the New states paradox occurs when 5 new litigators are added for the new court. Court: A B C Total Pending cases: 209 769 2, 022 3, 000

Solution Summary: The author explains that the New states paradox occurs when 5 new litigators are added for the new court.

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Whether the New states paradox occurs when 5 new litigators are added for the new court. Court: A B CTotalPending cases:2097692, 0223, 000

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Chapter 17 Solutions

Whether the New states paradox occurs when 5 new litigators are added for the new court.

Court: A B CTotalPending cases:2097692, 0223, 000