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: 16

Answer

Using Webster's method, each state is apportioned the following number of seats: State A is apportioned 42 congressional seats. State B is apportioned 67 congressional seats. State C is apportioned 89 congressional seats. State D is apportioned 116 congressional seats.

Work Step by Step

We can use the modified divisor of $d = 9.98$ to find the modified quota for each state. State A: $modified ~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{424}{9.98}$ $modified~quota = 42.48$ State B: $modified ~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{664}{9.98}$ $modified~quota = 66.53$ State C: $modified ~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{892}{9.98}$ $modified~quota = 89.38$ State D: $modified ~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{1162}{9.98}$ $modified~quota = 116.43$ Webster's method is an apportionment method that involves rounding each modified quota down to the nearest whole number if the fractional part is less than 0.5, and rounding each modified quota up to the nearest whole number if the fractional part is more than 0.5. Using Webster's method, each state is apportioned the following number of seats: State A is apportioned 42 congressional seats. State B is apportioned 67 congressional seats. State C is apportioned 89 congressional seats. State D is apportioned 116 congressional seats.
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