## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 13 - Voting and Apportionment - Chapter Summary, Review, and Test - Review Exercises - Page 889: 35

#### Answer

Using Adams's method, each clinic is apportioned the following number of doctors: Clinic A is apportioned 6 doctors. Clinic B is apportioned 8 doctors. Clinic C is apportioned 12 doctors. Clinic D is apportioned 14 doctors.

#### Work Step by Step

Let's use a modified divisor of $d = 52$ to find the modified quota for each clinic. Clinic A: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{275}{52}$ $modified~quota = 5.29$ Clinic B: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{392}{52}$ $modified~quota = 7.54$ Clinic C: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{611}{52}$ $modified~quota = 11.75$ Clinic D: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{724}{52}$ $modified~quota = 13.92$ Using Adams's method, the modified quota is rounded up to the nearest whole number. Each clinic is apportioned the following number of doctors: Clinic A is apportioned 6 doctors. Clinic B is apportioned 8 doctors. Clinic C is apportioned 12 doctors. Clinic D is apportioned 14 doctors. Note that the total number of doctors apportioned is 40, so using a modified divisor of 52 is acceptable.

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