Use the following information to answer the Questions
At the end of the lease on their apartment, Abe and Bonnie decide to rent separate places and so must make a fair division of the property they purchased together. The items to be divided and the point values each person places on them are given below. $$\begin{array} { l l l }
\text { Item } & \text { Abe's points } & \text { Bonnie's point } \
\text { Plant } & 10 & 10 \
\text { Bookcase } & 40 & 30 \
\text { Quilt } & 25 & 20 \
\text { Picture } & 25 & 40
\end{array}$$
-If Abe and Bonnie use the adjusted winner procedure to divide the property, how many points of value will each person think they end up with?
A) 55.67
B) 76.67
C) 54.23
D) 56.50

Question

Use the following information to answer the Questions
At the end of the lease on their apartment, Abe and Bonnie decide to rent separate places and so must make a fair division of the property they purchased together. The items to be divided and the point values each person places on them are given below. $$\begin{array} { l l l } 
\text { Item } & \text { Abe's points } & \text { Bonnie's point } \
\text { Plant } & 10 & 10 \
\text { Bookcase } & 40 & 30 \
\text { Quilt } & 25 & 20 \
\text { Picture } & 25 & 40
\end{array}$$
-If Abe and Bonnie use the adjusted winner procedure to divide the property, how many points of value will each person think they end up with?
A) 55.67
B) 76.67
C) 54.23
D) 56.50

Quizplus · Accepted Answer

To find a fair division of the property using the adjusted winner procedure, we follow these steps:
1. Calculate the total points each person gives to all the items: Abe = 100 (10 + 40 + 25 + 25) and Bonnie = 100 (10 + 30 + 20 + 40).
2. Calculate the average points per item for each person: Abe = 25 (100/4) and Bonnie = 25 (100/4).
3. Calculate the excess points for each item: Plant = 0 (10 - 25), Bookcase = 15 (40 - 25), Quilt = 0 (25 - 25), Picture = 15 (40 - 25).
4. Add up the excess points for each person: Abe = 30 (0 + 15 + 0 + 15) and Bonnie = -30 (0 - 15 + 0 - 15).
5. Divide the excess points equally between the two people: Abe = 15 (30/2) and Bonnie = -15 (-30/2).
6. Add the adjusted points to the original points for each person: Abe = 40 (10 + 40 + 25 + 25 + 15) and Bonnie = 55 (10 + 30 + 20 + 40 - 15).
Therefore, each person thinks they end up with 40 points of value, which is the sum of their adjusted points. The correct answer is B, 76.67, which is the sum of both people's adjusted points divided by 2.

Use the Following Information to Answer the Questions at the End

Use the Following Information to Answer the Questions
at the End