## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 13 - Voting and Apportionment - 13.3 Apportionment Method - Exercise Set 13.3 - Page 875: 13

#### Answer

Using Adams's method, the shares are apportioned to each person as follows: Person A is apportioned 12 shares. Person B is apportioned 10 shares. Person C is apportioned 8 shares.

#### Work Step by Step

We can find the total amount of contributions. total contributions = \$795 + \$705 + \$525 total contributions = \$2025 We can find the standard divisor. $standard ~divisor = \frac{total ~contributions}{shares}$ $standard ~divisor = \frac{2025}{30}$ $standard ~divisor = 67.5$ If we use the standard divisor and round each standard quota up to the nearest whole number, the sum of the shares will be more than 30 shares. To obtain a sum of 30 shares, we need to find a modified divisor that is slightly more than the standard divisor. Let's choose a modified divisor of 72. 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 person. Person A: $modified~quota = \frac{contribution}{modified~divisor}$ $modified~quota = \frac{795}{72}$ $modified~quota = 11.04$ Person B: $modified~quota = \frac{contribution}{modified~divisor}$ $modified~quota = \frac{705}{72}$ $modified~quota = 9.79$ Person C: $modified~quota = \frac{contribution}{modified~divisor}$ $modified~quota = \frac{525}{72}$ $modified~quota = 7.29$ 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 12 shares. Person B is apportioned 10 shares. Person C is apportioned 8 shares. Note that the sum of the apportioned shares is 30, so using a modified divisor of 72 is acceptable.

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