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: 12

Answer

Using Adams's method, the shares are apportioned to each person as follows: Person A is apportioned 19 shares. Person B is apportioned 2 shares. Person C is apportioned 3 shares. Person D is apportioned 36 shares.

Work Step by Step

Using the modified divisor of $d = 108$, we can find the modified quota for each person. Person A: $modified~quota = \frac{contribution}{modified~divisor}$ $modified~quota = \frac{2013}{108}$ $modified~quota = 18.64$ Person B: $modified~quota = \frac{contribution}{modified~divisor}$ $modified~quota = \frac{187}{108}$ $modified~quota = 1.73$ Person C: $modified~quota = \frac{contribution}{modified~divisor}$ $modified~quota = \frac{290}{108}$ $modified~quota = 2.69$ Person D: $modified~quota = \frac{contribution}{modified~divisor}$ $modified~quota = \frac{3862}{108}$ $modified~quota = 35.76$ Using Adams's method, we apportion the shares by rounding the modified quota up to the nearest whole number. The shares are apportioned to each person as follows: Person A is apportioned 19 shares. Person B is apportioned 2 shares. Person C is apportioned 3 shares. Person D is apportioned 36 shares. Note that the sum of the apportioned shares is 60.
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