Explanation Given information: The English enrollments at five high schools in the Santa Rosa Unified School District are as follows: High Schools Population Elsie Allen 154 Maria Carillo 142 Montgomery 165 Piner 307 Santa Rosa 231 Total 999 Suppose that 45 copies of the instructional video are to be allocated to the schools by using Hamilton’s plan and the school population. Formula used: STANDARD DIVISOR = TOTAL POPULATION NUMBER OF SHARES STANDARD QUOTA = TOTAL POPULATION STANDARD DIVISOR Calculation: In Hamilton’s plan, calculate the standard quota ( q ) for each district and round down to the nearest integer. Give additional seats, one at a time to the district with the largest fractional parts of their standard quotas. The total production is 999 . The number of copies of an important instructional video is 45 . Substitute the values of the total production and the number of copies of an important instructional video in the formula of the standard divisor d , d = 999 45 = 22.2 Therefore, the standard divisor is 22.2 . Substitute the values of the population for each high school and standard divisor d in the formula of standard quota. The values of the standard quota of each high schools in the Santa Rosa Unified School District are summarized in the below table: High Schools Standard Quota ( q ) Lower Quota Elsie Allen 154 22.2 = 6.936937 ≈ 6.94 6 Maria Carillo 142 22.2 = 6.396396 ≈ 6.40 6 Montgomery 165 22.2 = 7.432432 ≈ 7.43 7 Piner 307 22.2 = 13.82883 ≈ 13.83 13 Santa Rosa 231 22.2 = 10.40541 ≈ 10.41 10 Add these lower quotas together: 6 + 6 + 7 + 13 + 10 = 42 . Lower quotas total is 42 but the number of copies of videos is 45 , therefore check the school with the largest fractional parts of their standard quotas. The largest fractional parts of standard quotas of three schools are: Elsie Allen is 0.94 , Montgomery is 0.43 and Piner is 0.83 , so give one additional copy of the video to Elsie Allen, Montgomery, and Piner. Following is the table with the additional copy of the video. High Schools Standard Quota ( q ) Lower Quota Fractional part Hamilton's plan Elsie Allen 154 22.2 = 6.936937 ≈ 6.94 6 0.94 6 + 1 = 7 Maria Carillo 142 22.2 = 6.396396 ≈ 6.40 6 0.40 6 Montgomery 165 22.2 = 7.432432 ≈ 7.43 7 0.43 7 + 1 = 8 Piner 307 22.2 = 13.82883 ≈ 13.83 13 0.83 13 + 1 = 14 Santa Rosa 231 22.2 = 10.40541 ≈ 10.41 10 0.41 10 By adding Hamilton’s plan, it becomes 7 + 6 + 8 + 14 + 10 = 45 And the number of copies of an important instructional video is 45

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 47PS

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Whether the Alabama paradox is illustrated or not if new video added so that 46 videos are allocated to schools by using Hamilton’s plan.

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Chapter 17.4, Problem 46PS

Chapter 17.4, Problem 48PS

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Chapter 17 Solutions

Nature of Mathematics (MindTap Course List)

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 Alabama paradox is illustrated or not if new video added so that 46 videos are allocated to schools by using Hamilton’s plan.

Solution Summary: The author explains that the Alabama paradox is not illustrated if new video is added so that 46 videos are allocated to schools using Hamilton's plan.

Whether the Alabama paradox is illustrated or not if new video added so that 46 videos are allocated to schools by using Hamilton’s plan.

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Chapter 17 Solutions