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 point value does Andi end with? $$\begin{array} { l l l }
\text { Object } & \text { Andi's points } & \text { Toni's points } \
\text { Car } & 35 & 45 \
\text { House } & 40 & 30 \
\text { Boat } & 25 & 25
\end{array}$$
A) 65
B) 55
C) 50
D) 60

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 point value does Andi end with? $$\begin{array} { l l l } 
\text { Object } & \text { Andi's points } & \text { Toni's points } \
\text { Car } & 35 & 45 \
\text { House } & 40 & 30 \
\text { Boat } & 25 & 25
\end{array}$$
A) 65
B) 55
C) 50
D) 60

Quizplus · Accepted Answer

To use the adjusted winner procedure, we first find the total points each person has:
Andi: $35+40+25=100$
Toni: $45+30+25=100$
Then, we find the "fair share" for each person. To do this, we add up the total points and divide by 2:
Fair share: $(35+45+40+30+25+25)/2=100$
Now, we "adjust" the points by subtracting each person's fair share from their total points:
Andi's adjusted points: $100-100=0$
Toni's adjusted points: $100-100=0$
Since both Andi and Toni have the same adjusted points, we need to add a tiebreaker. We do this by comparing the points they each would have if they got to keep one less item.

If Andi keeps the car and the boat, he has a total of $35+25=60$ points. If Toni keeps the house and the boat, he has a total of $30+25=55$ points. Since Andi has the higher total in this situation, he gets to keep the car and the boat.

Therefore, the final point value for Andi is $0+40+0=40$.

Subtracting this from his original point total, we get: $100-40=60$.

So, the answer is D) 60.

Andi and Toni Must Make Fair Division of a Car