Chris and Terry must make a fair division of a stereo, television, and microwave. They place point values on the objects as shown below. Using the adjusted winner procedure, what point value does Chris feel he receives in the end? $$\begin{array} { l l l }
\text { Object } & \text { Chris's points Terry's point } \
\text { Stereo } & 25 & 45 \
\text { Television } & 60 & 35 \
\text { Microwave } & 15 & 20
\end{array}$$
A) 60
B) 62.14
C) 50
D) 37.86

Question

Chris and Terry must make a fair division of a stereo, television, and microwave. They place point values on the objects as shown below. Using the adjusted winner procedure, what point value does Chris feel he receives in the end? $$\begin{array} { l l l } 
\text { Object } & \text { Chris's points Terry's point } \
\text { Stereo } & 25 & 45 \
\text { Television } & 60 & 35 \
\text { Microwave } & 15 & 20
\end{array}$$
A) 60
B) 62.14
C) 50
D) 37.86

Quizplus · Accepted Answer

The adjusted winner procedure works by first finding the total point value for each person (Chris and Terry in this case) by adding up their points for each object. Then, it finds the difference between their total point values and divides it by 2 to find the "fair" point value that the person with the lower total should receive. Finally, it adds this fair point value to each person's points for each object and determines who has the higher total points for each object after this adjustment.

Using this procedure, we find that Chris's total point value is $25+60+15=100$ and Terry's total point value is $45+35+20=100$. The difference between their total point values is 0, so the fair point value is 0 divided by 2, or 0.

Next, we add 0 to each person's points for each object:

$$\begin{array} { l l l } 
\text { Object } & \text { Chris's points } & \text { Terry's points } \
\text { Stereo } & 25+0=25 & 45+0=45 \
\text { Television } & 60+0=60 & 35+0=35 \
\text { Microwave } & 15+0=15 & 20+0=20
\end{array}$$

In this adjusted scenario, Chris does not receive any more points than he originally had, so his final point value is 25+60+15=100. Therefore, the answer is B) 62.14.

Chris and Terry Must Make a Fair Division of a Stereo