Andi and Toni must make fair division of a car, a house, and a boat. The point values they place on the objects are given below. Using the adjusted winner procedure, what does Andi end with? $$\begin{array} { l l l }
\text { Object } & \text { Andi's points } & \text { Toni's points } \
\text { Car } & 35 & 45 \
\text { House } & 40 & 30 \
\text { Boat } & 25 & 25
\end{array}$$

Question

Andi and Toni must make fair division of a car, a house, and a boat. The point values they place on the objects are given below. Using the adjusted winner procedure, what does Andi end with? $$\begin{array} { l l l } 
\text { Object } & \text { Andi's points } & \text { Toni's points } \
\text { Car } & 35 & 45 \
\text { House } & 40 & 30 \
\text { Boat } & 25 & 25
\end{array}$$

Quizplus · Accepted Answer

Step 1: Find the total point value for each person.

Andi's total points: 35+40+25 = 100
Toni's total points: 45+30+25 = 100

Step 2: Find the difference between each person's total point value and the point value of the object they receive.

For Andi:
Car: 100-35 = 65
House: 100-40 = 60
Boat: 100-25 = 75

For Toni:
Car: 100-45 = 55
House: 100-30 = 70
Boat: 100-25 = 75

Step 3: Calculate the adjusted winner for each object by adding half of the difference from Step 2 to the original point value of the object.

Adjusted winner for the car:
Andi: 35 + (65/2) = 67.5
Toni: 45 + (55/2) = 67.5

Adjusted winner for the house:
Andi: 40 + (60/2) = 70
Toni: 30 + (70/2) = 65

Adjusted winner for the boat:
Andi: 25 + (75/2) = 62.5
Toni: 25 + (75/2) = 62.5

Step 4: The person with the highest adjusted winner for each object gets that object.

Andi and Toni both have the highest adjusted winner for the car, so they will need to divide it further.

For the house, Andi has the highest adjusted winner, so they will give the house to Andi.

For the boat, Andi has the highest adjusted winner, so they will give the boat to Andi.

Since Andi and Toni both have the highest adjusted winner for the car, they will need to divide it further. Using the same process as before, we get:

Adjusted winner for the car (Andi):
Andi: 35 + (65/4) = 51.25
Toni: 45 + (55/4) = 63.75

Adjusted winner for the car (Toni):
Andi: 35 + (65/4) = 51.25
Toni: 45 + (55/4) = 63.75

Toni has the highest adjusted winner for the car, so they will give 3/4 of the car to Toni and 1/4 to Andi.

Therefore, Andi gets the house and 3/5 of the boat. The answer is D.

Andi and Toni Must Make Fair Division of a Car