Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 13 - Voting and Apportionment - 13.3 Apportionment Method - Exercise Set 13.3: 11

Answer

Using Adams's method, the officers are apportioned to the precincts as follows: Precinct A is apportioned 28 officers. Precinct B is apportioned 33 officers. Precinct C is apportioned 53 officers. Precinct D is apportioned 15 officers. Precinct E is apportioned 22 officers. Precinct F is apportioned 29 officers.

Work Step by Step

Using the modified divisor of $d = 16$, we can find the modified quota for each precinct. Precinct A: $modified~quota = \frac{crimes}{modified~divisor}$ $modified~quota = \frac{446}{16}$ $modified~quota = 27.88$ Precinct B: $modified~quota = \frac{crimes}{modified~divisor}$ $modified~quota = \frac{526}{16}$ $modified~quota = 32.88$ Precinct C: $modified~quota = \frac{crimes}{modified~divisor}$ $modified~quota = \frac{835}{16}$ $modified~quota = 52.19$ Precinct D: $modified~quota = \frac{crimes}{modified~divisor}$ $modified~quota = \frac{227}{16}$ $modified~quota = 14.19$ Precinct E: $modified~quota = \frac{crimes}{modified~divisor}$ $modified~quota = \frac{338}{16}$ $modified~quota = 21.13$ Precinct F: $modified~quota = \frac{crimes}{modified~divisor}$ $modified~quota = \frac{456}{16}$ $modified~quota = 28.5$ Using Adams's method, we apportion the officers by rounding the modified quota up to the nearest whole number. The officers are apportioned to the precincts as follows: Precinct A is apportioned 28 officers. Precinct B is apportioned 33 officers. Precinct C is apportioned 53 officers. Precinct D is apportioned 15 officers. Precinct E is apportioned 22 officers. Precinct F is apportioned 29 officers. Note that the sum of the apportioned officers is 180.
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