Explanation Given information: College town population of citizens is as follows. District Population North 18 , 200 South 12 , 900 East 17 , 600 West 13 , 300 Number of representatives is 16 . Formula used: STANDARD DIVISOR = TOTAL POPULATION NUMBER OF SHARES STANDARD QUOTA = TOTAL POPULATION STANDARD DIVISOR Use the following steps in HH’s plan. Step-1: Calculate the standard quota ( q ) using standard divisor for each state. Step-2: Find lower quota ( a ) and upper quota ( b ) . Step-3: Find geometric mean a b . Step-4: Round the standard quotas down: if the fractional part < a b and round up if fractional part is ≥ a b Find the total of rounded numbers; the total will be correct or it will not. Step-5: If the total is not correct, lower or raise the standard divisor in small increments to find a modified divisor that will give modified quota that provide the appropriate total. Given number of representatives is 16 . Suppose standard divisor is denoted by d . Substitute the values of the total population and number of representatives in the formula of standard divisor d , d = 62 , 000 16 = 3 , 875 Therefore, the standard divisor is d = 3 , 875 Divide the population of each district by standard divisor ( d ) to find the standard quota ( q ) for each district

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 17.3, Problem 55PS

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The HH’s apportionment plan assuming that there must be 16 representatives for the following apportionment problem.

DistrictPopulationNorth18,200South12,900East17,600West13,300

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Chapter 17.3, Problem 54PS

Chapter 17.3, Problem 56PS

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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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The HH’s apportionment plan assuming that there must be 16 representatives for the following apportionment problem. District Population North 18 , 200 South 12 , 900 East 17 , 600 West 13 , 300

Solution Summary: The author explains HH's apportionment plan using the following steps: Calculate the standard quota (q) and find geometric mean

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The HH’s apportionment plan assuming that there must be 16 representatives for the following apportionment problem.

DistrictPopulationNorth18,200South12,900East17,600West13,300

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Chapter 17 Solutions

The HH’s apportionment plan assuming that there must be 16 representatives for the following apportionment problem. District Population North 18 , 200 South 12 , 900 East 17 , 600 West 13 , 300

Solution Summary: The author explains HH's apportionment plan using the following steps: Calculate the standard quota (q) and find geometric mean

Concept explainers

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The HH’s apportionment plan assuming that there must be 16 representatives for the following apportionment problem. DistrictPopulationNorth18,200South12,900East17,600West13,300

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Chapter 17 Solutions

The HH’s apportionment plan assuming that there must be 16 representatives for the following apportionment problem.

DistrictPopulationNorth18,200South12,900East17,600West13,300