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: 1

Answer

(a) The standard divisor is 20 (thousand). There are 20,000 people for each seat in congress. (b) State A's standard quota is 6.9 State B's standard quota is 13.3 State C's standard quota is 26.7 State D's standard quota is 33.1 (c) State A's lower quota is 6 State A's upper quota is 7 State B's lower quota is 13 State B's upper quota is 14 State C's lower quota is 26 State C's upper quota is 27 State D's lower quota is 33 State D's upper quota is 34

Work Step by Step

(a) We can find the standard divisor. $standard~divisor = \frac{total ~population}{number~of~ items}$ $standard~divisor = \frac{1600}{80}$ $standard~divisor = 20$ The standard divisor is 20 (thousand). There are 20,000 people for each seat in congress. (b) We can find each state's standard quota. The standard quota of each state is the state's population divided by the standard divisor. State A: $standard ~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{138}{20}$ $standard~quota = 6.9$ State A's standard quota is 6.9 State B: $standard ~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{266}{20}$ $standard~quota = 13.3$ State B's standard quota is 13.3 State C: $standard ~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{534}{20}$ $standard~quota = 26.7$ State C's standard quota is 26.7 State D: $standard ~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{662}{20}$ $standard~quota = 33.1$ State D's standard quota is 33.1 (c) The lower quota is the standard quota rounded down to the nearest whole number. The upper quota is the standard quota rounded up to the nearest whole number. We can find each state's lower quota and upper quota. State A's standard quota is 6.9 State A's lower quota is 6 State A's upper quota is 7 State B's standard quota is 13.3 State B's lower quota is 13 State B's upper quota is 14 State C's standard quota is 26.7 State C's lower quota is 26 State C's upper quota is 27 State D's standard quota is 33.1 State D's lower quota is 33 State D's upper quota is 34
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