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Alice, Bob, and Carlos are dividing among themselves a set of common assets equally
Chapter 3, Problem 2(choose chapter or problem)
Alice, Bob, and Carlos are dividing among themselves a set of common assets equally owned by the three of them. The assets are divided into three shares (\(s_{1}, s_{2}\), and \(s_3\)). Table 13 shows the values of the shares to each player expressed as a percent of the total value of the assets.
(a) Which of the shares are fair shares to Alice?
(b) Which of the shares are fair shares to Bob?
(c) Which of the shares are fair shares to Carlos?
(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?
\(\begin{array}{l|c|c|c}
& \boldsymbol{s}_{\mathbf{1}} & \boldsymbol{s}_{\mathbf{2}} & \boldsymbol{s}_{\mathbf{3}} \\
\hline \text { Alice } & 38 \% & 28 \% & 34 \% \\
\hline \text { Bob } & 33 \frac{1}{3} \% & 33 \frac{1}{3} \% & 33 \frac{1}{3} \% \\
\hline \text { Carlos } & 34 \% & 40 \% & 26 \%
\end{array}\)
Questions & Answers
QUESTION:
Alice, Bob, and Carlos are dividing among themselves a set of common assets equally owned by the three of them. The assets are divided into three shares (\(s_{1}, s_{2}\), and \(s_3\)). Table 13 shows the values of the shares to each player expressed as a percent of the total value of the assets.
(a) Which of the shares are fair shares to Alice?
(b) Which of the shares are fair shares to Bob?
(c) Which of the shares are fair shares to Carlos?
(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?
\(\begin{array}{l|c|c|c}
& \boldsymbol{s}_{\mathbf{1}} & \boldsymbol{s}_{\mathbf{2}} & \boldsymbol{s}_{\mathbf{3}} \\
\hline \text { Alice } & 38 \% & 28 \% & 34 \% \\
\hline \text { Bob } & 33 \frac{1}{3} \% & 33 \frac{1}{3} \% & 33 \frac{1}{3} \% \\
\hline \text { Carlos } & 34 \% & 40 \% & 26 \%
\end{array}\)
Step 1 of 4
Alice, Bob, and Carlos are dividing among themselves a set of common assets equally owned by the three of them. The assets are divided into three shares \(\left( {{s_1},{s_2},{s_3}} \right)\).
The table shows the values of the shares to each player expressed as a percent of the total value of the assets as,
\(\begin{array}{l|c|c|c} & \boldsymbol{s}_{\mathbf{1}} & \boldsymbol{s}_{\mathbf{2}} & \boldsymbol{s}_{\mathbf{3}} \\ \hline \text { Alice } & 38 \% & 28 \% & 34 \% \\ \hline \text { Bob } & 33 \frac{1}{3} \% & 33 \frac{1}{3} \% & 33 \frac{1}{3} \% \\ \hline \text { Carlos } & 34 \% & 40 \% & 26 \% \end{array}\)