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Angie, Bev, Ceci, and Dina are dividing among themselves a set of common assets equally
Chapter 3, Problem 3(choose chapter or problem)
Angie, Bev, Ceci, and Dina are dividing among themselves a set of common assets equally owned by the four of them. The assets are divided into four shares \(\left(s_{1}, s_{2}, s_{3}, \text { and } s_{4}\right)\). Table 14 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 Angie?
(b) Which of the shares are fair shares to Bev?
(c) Which of the shares are fair shares to Ceci?
(d) Which of the shares are fair shares to Dina?
(e) Find all possible fair divisions of the assets using \(s_{1}, s_{2}, s_{3}\), and \(s_{4}\) as shares.
\(\begin{array}{|l|l|l|l|l|} \hline & s_{1} & s_{2} & s_{3} & s_{4} \\ \hline \text { Angie } & 22 \% & 26 \% & 28 \% & 24 \% \\ \hline \text { Bev } & 25 \% & 26 \% & 22 \% & 27 \% \\ \hline \text { Ceci } & 20 \% & 30 \% & 27 \% & 23 \% \\ \hline \text { Dina } & 25 \% & 25 \% & 25 \% & 25 \% \\ \hline \end{array}\)
TABLE 14Questions & Answers
QUESTION:
Angie, Bev, Ceci, and Dina are dividing among themselves a set of common assets equally owned by the four of them. The assets are divided into four shares \(\left(s_{1}, s_{2}, s_{3}, \text { and } s_{4}\right)\). Table 14 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 Angie?
(b) Which of the shares are fair shares to Bev?
(c) Which of the shares are fair shares to Ceci?
(d) Which of the shares are fair shares to Dina?
(e) Find all possible fair divisions of the assets using \(s_{1}, s_{2}, s_{3}\), and \(s_{4}\) as shares.
\(\begin{array}{|l|l|l|l|l|} \hline & s_{1} & s_{2} & s_{3} & s_{4} \\ \hline \text { Angie } & 22 \% & 26 \% & 28 \% & 24 \% \\ \hline \text { Bev } & 25 \% & 26 \% & 22 \% & 27 \% \\ \hline \text { Ceci } & 20 \% & 30 \% & 27 \% & 23 \% \\ \hline \text { Dina } & 25 \% & 25 \% & 25 \% & 25 \% \\ \hline \end{array}\)
TABLE 14 ANSWER:Step 1 of 4
The table showing the percentages is:
\(\begin{array}{|l|l|l|l|l|} \hline & s_{1} & s_{2} & s_{3} & s_{4} \\ \hline \text { Angie } & 22 \% & 26 \% & 28 \% & 24 \% \\ \hline \text { Bev } & 25 \% & 26 \% & 22 \% & 27 \% \\ \hline \text { Ceci } & 20 \% & 30 \% & 27 \% & 23 \% \\ \hline \text { Dina } & 25 \% & 25 \% & 25 \% & 25 \% \\ \hline \end{array}\)
Let us assume the total value of assets is 100.
Calculating value of \(S_{1}\) for Angie:
\(\begin{aligned} 22 \% & =\frac{22 \times 100}{100} \\ & =22 \end{aligned}\)
Similarly, solve the rest and get the values of assets as:
\(\begin{array}{|l|l|l|l|l|} \hline & s_{1} & s_{2} & s_{3} & s_{4} \\ \hline \text { Angie } & 22 & 26 & 28 & 24 \\ \hline \text { Bev } & 25 & 26 & 22 & 27 \\ \hline \text { Ceci } & 20 & 30 & 27 & 23 \\ \hline \text { Dina } & 25 & 25 & 25 & 25 \\ \hline \end{array}\)