Explanation A university has two colleges, Letters and Sciences ( L ) , and Education ( E ) , with enrollments as shown in the following table. College: L E Total Entollment: 8, 955 1, 045 10, 000 Each year, 100 scholarships are awarded to the students. The total number of enrollments is 10 , 000 . The total number of scholarships is 100 . Therefore, the standard divisor d = 10 , 000 100 = 100 . Now divide the number of enrollments of each college by the standard divisor ( d = 100 ) to get the standard quota ( q ) for each college. Then round the standard quotas down to the nearest integer, but each college gets at least one scholarship. Therefore, the number of scholarships assign to each college is as follows: College Enrollments Standard Quota, q Lower Quota L 8, 955 8, 955 100 =89 .55 89 E 1,045 1,045 100 =10 .45 10 Total 10, 000 99 Here the total numbers of scholarships are 100 and the total of the lower quotas is 99 , that is one scholarship does not assign to any college. 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 the fraction part of college L is larger than college E , one scholarship is assigned to the college L . Therefore, the number of scholarships assign to each college according to Hamilton’s plan is as follows: College Enrollments Lower Quota Hamilton's Plan L 8, 955 89 89 + 1 = 90 E 1, 045 10 10 Total 10, 000 99 100 Now, the college P established with 525 students and added 5 new scholarships. So enrollments are as follow: College: L E P Total Enrollment: 8, 955 1, 045 525 10, 525 The total number of enrollments is 10 , 525

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ISBN: 9780357325865

Author: SMITH

Publisher: CENGAGE L

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Chapter 17.4, Problem 36PS

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Whether the New states paradox occurs or not, when 105 scholarships are awarded to the students with following enrollments.

College:LEPTotalEnrollment:8, 9551, 04552510, 525.

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Chapter 17.4, Problem 35PS

Chapter 17.4, Problem 37PS

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Chapter 17 Solutions

NATURE OF MATHEMATICS LL + WEBASSIGN

Ch. 17.1 - Prob. 1PS Ch. 17.1 - Prob. 2PS Ch. 17.1 - Prob. 3PS Ch. 17.1 - Prob. 4PS Ch. 17.1 - Prob. 5PS Ch. 17.1 - Prob. 6PS Ch. 17.1 - Prob. 7PS Ch. 17.1 - Prob. 8PS Ch. 17.1 - Prob. 9PS Ch. 17.1 - Prob. 10PS

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Whether the New states paradox occurs or not, when 105 scholarships are awarded to the students with following enrollments. College: L E P Total Enrollment: 8, 955 1, 045 525 10, 525 .

Solution Summary: The author explains how the apportionment shift from college L to the college — each year, 100 scholarships are awarded.

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Whether the New states paradox occurs or not, when 105 scholarships are awarded to the students with following enrollments.

College:LEPTotalEnrollment:8, 9551, 04552510, 525.

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Chapter 17 Solutions

Whether the New states paradox occurs or not, when 105 scholarships are awarded to the students with following enrollments. College: L E P Total Enrollment: 8, 955 1, 045 525 10, 525 .

Solution Summary: The author explains how the apportionment shift from college L to the college — each year, 100 scholarships are awarded.

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Whether the New states paradox occurs or not, when 105 scholarships are awarded to the students with following enrollments. College:LEPTotalEnrollment:8, 9551, 04552510, 525.

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Chapter 17 Solutions

Whether the New states paradox occurs or not, when 105 scholarships are awarded to the students with following enrollments.

College:LEPTotalEnrollment:8, 9551, 04552510, 525.