   # Elementary School Teachers The following table shows the number of fifth and sixth grade teachers in a school district and the number of students in the two grades. The number of teachers for each of the grade levels was determined by using the Huntington-Hill apportionment method. The district has decided to hire a new teacher for either the fifth or the sixth grade. a. Use the apportionment principle to determine to which grade the new teacher should be assigned. b. Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned. How does this result compare with the result in part a? ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.1, Problem 21ES
Textbook Problem
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## Elementary School Teachers The following table shows the number of fifth and sixth grade teachers in a school district and the number of students in the two grades. The number of teachers for each of the grade levels was determined by using the Huntington-Hill apportionment method. The district has decided to hire a new teacher for either the fifth or the sixth grade.a. Use the apportionment principle to determine to which grade the new teacher should be assigned.b. Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned. How does this result compare with the result in part a?

To determine

(a)

Use the apportionment principle to determine to which grade the new teacher should be assigned.

### Explanation of Solution

Given Information:

 Number of teachers Number of students Fifth grade 19 604 Sixth grade 21 698

Concept used:

Absolute unfairness of apportionment = Sixth Grade Average constituency  fith grade Average constituencyCalculation:

First find out the average constituency to calculate absolute unfairness which decide which grade the new teacher should be assigned,

 Number of Teachers Number of Students Average Constituency Fifth Grade 19 604 60419≈31 Sixth grade 21 698 69821≈33

Since, we have to calculate new average constituency consider that one teacher increases in every grade, therefore

 Number of Teachers Number of Students Average Constituency Fifth Grade 19 604
To determine

(b)

Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned. How does this result compare with the result in part a?

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