Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - Chapter Summary, Review, and Test - Review Exercises: 39

Answer

Using Adams's method, each state is apportioned the following number of seats: State A is apportioned 14 seats. State B is apportioned 42 seats. State C is apportioned 63 seats. State D is apportioned 81 seats.

Work Step by Step

We can find the total population. total population = 3320 + 10,060 + 15,020 + 19,600 total population = 48,000 We can find the standard divisor. $standard~divisor = \frac{total~population}{number~of~ seats}$ $standard~divisor = \frac{48,000}{200}$ $standard~divisor = 240$ The standard divisor is 240 We can find the standard quota for each state. State A: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{3320}{240}$ $standard~quota = 13.83$ State B: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{10,060}{240}$ $standard~quota = 41.92$ State C: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{15,020}{240}$ $standard~quota = 62.58$ State D: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{19,600}{240}$ $standard~quota = 81.67$ Adams's method is an apportionment method that involves rounding each quota up to the nearest whole number. If each state is apportioned its upper quota, then the total number of apportioned seats is 14 + 42 + 63 + 82, which is 201 seats. To obtain a sum of 200 seats, we need to use a modified divisor that is slightly more than the standard divisor of 240. Let's choose a modified divisor of 242. Note that it may require a bit of trial-and-error to find a modified divisor that works. We can find the modified quota for each state. State A: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{3320}{242}$ $modified~quota = 13.72$ State B: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{10,060}{242}$ $modified~quota = 41.57$ State C: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{15,020}{242}$ $modified~quota = 62.07$ State D: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{19,600}{242}$ $modified~quota = 80.99$ Using Adams's method, the modified quota is rounded up to the nearest whole number. Each state is apportioned the following number of seats: State A is apportioned 14 seats. State B is apportioned 42 seats. State C is apportioned 63 seats. State D is apportioned 81 seats. Note that the total number of seats apportioned is 200, so using a modified divisor of 242 is acceptable.
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