Student's Solutions Manual For Excursions In Modern Mathematics Format: Paperback
Student's Solutions Manual For Excursions In Modern Mathematics Format: Paperback
9th Edition
ISBN: 9780134469133
Author: Tannenbaum, Peter
Publisher: Prentice Hall
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Textbook Question
Chapter 3, Problem 1E

Henry, Tom, and Fred are breaking up their partnership and dividing among themselves the partnership’s real estate assets equally owned by the three of them. The assets are divided into three shares ( s 1 , s 2  and  s 3 ) . Table 3-12 shows the values of the shares to each player expressed as a percent of the total value of the assets.

Table 3-12

S1 S2 S3
Henry 25 % 40 % 35 %
Tom 28 % 35 % 37 %
Fred 33 1 3 % 33 1 3 % 33 1 3 %

a. Which of the shares are fair shares to Henry?

b. Which of the shares are fair shares to Tom?

c. Which of the shares are fair shares to Fred?

d. Find all possible fair divisions of the assets using s 1 , s 2  and  s 3 as shares.

e. Of the fair divisions found in (d), which one is the best?

Expert Solution
Check Mark
To determine

(a)

To find:

Fair shares for Henry from the given table.

Answer to Problem 1E

Solution:

Fair shares for Henry are s2 and s3.

Explanation of Solution

Given:

The given table for value of shares to each player is shown in table 1.

Table 1

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

Fair share for each player should be 100N%, where N is the total number of players.

Calculation:

The value of shares to each player is,

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

There are total 3 players in which assets will be divided so the fair share for each player would be 1003% or 3313%.

Then according to table fair shares for Henry will be s2 and s3 because these are greater than fair share.

Conclusion:

Thus, fair shares for Henry are s2 and s3.

Expert Solution
Check Mark
To determine

(b)

To find:

Fair shares for Tom from the given table.

Answer to Problem 1E

Solution:

Fair shares for Tom are s2 and s3.

Explanation of Solution

Given:

The given table for value of shares to each player is shown in table 1.

Table 1

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

Fair share for each player should be 100N%, where N is the total number of players.

Calculation:

The value of shares to each player is,

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

There are total 3 players in which assets will be divided so the fair share for each player would be 1003% or 3313%.

Then according to table fair shares for Tom will be s2 and s3 because these are greater than fair share.

Conclusion:

Thus, fair shares for Tom are s2 and s3.

Expert Solution
Check Mark
To determine

(c)

To find:

Fair shares for Fred from the given table.

Answer to Problem 1E

Solution:

Fair shares for Fred are s1,s2 and s3.

Explanation of Solution

Given:

The given table for value of shares to each player is shown in table 1.

Table 1

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

Fair share for each player should be 100N%, where N is the total number of players.

Calculation:

The value of shares to each player is,

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

There are total 3 players in which assets will be divided so the fair share for each player would be 1003% or 3313%.

Then according to table fair shares for Fred will be s1,s2 and s3 because all are equal to the fair share.

Conclusion:

Thus, fair shares for Fred are s1,s2 and s3.

Expert Solution
Check Mark
To determine

(d)

To find:

All possible fair divisions of the assets using given table.

Answer to Problem 1E

Solution:

The fair division of assets is possible in two ways:

i. Henry gets s2, Tom gets s3, and Fred gets s1.

ii. Henry gets s3, Tom gets s2, and Fred gets s1.

Explanation of Solution

Given:

The given table for value of shares to each player is shown in table 1.

Table 1

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

Fair share for each player should be 100N%, where N is the total number of players.

Calculation:

The value of shares to each player is,

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

There are total 3 players in which assets will be divided so the fair share for each player would be 1003% or 3313%.

Henry and Tom both have fair shares s2 and s3 and Fred has all three shares are fair. So the fair division of assets is possible in two ways:

i. Henry gets s2, Tom gets s3, and Fred gets s1.

ii. Henry gets s3, Tom gets s2, and Fred gets s1.

Conclusion:

Thus, the fair division of assets is possible in two ways:

i. Henry gets s2, Tom gets s3, and Fred gets s1.

ii. Henry gets s3, Tom gets s2, and Fred gets s1.

Expert Solution
Check Mark
To determine

(e)

To find:

The best fair division among the fair divisions found in part (4).

Answer to Problem 1E

Solution:

The best fair division of assets is: Henry gets s2, Tom gets s3 and Fred gets s1.

Explanation of Solution

Given:

The given table for value of shares to each player is shown in table 1.

Table 1

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

Fair share for each player should be 100N%, where N is the total number of players.

Calculation:

The value of shares to each player is,

S1 S2 S3
Henry 25% 40% 35%
Tom 28% 35% 37%
Fred 3313% 3313% 3313%

There are total 3 players in which assets will be divided so the fair share for each player would be 1003% or 3313%.

Henry and Tom both have fair shares s2 and s3 and Fred has all three shares are fair. So the fair division of assets is possible in two ways:

i. Henry gets s2, Tom gets s3, and Fred gets s1.

ii. Henry gets s3, Tom gets s2, and Fred gets s1.

The best fair division is the one in which players are more happy. Henry would be more happy in choice (i) and Tom also would be more happy in choice (i). Fred is happy in equally in both choices.

So the best fair division of assets is: Henry gets s2, Tom gets s3, and Fred gets s1.

Conclusion:

Thus, the best fair division of assets is: Henry gets s2, Tom gets s3, and Fred gets s1.

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Chapter 3 Solutions

Student's Solutions Manual For Excursions In Modern Mathematics Format: Paperback

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