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Allen, Brady, Cody, and Diane are sharing a cake valued at $20 using the lone-divider
Chapter 3, Problem 26(choose chapter or problem)
Allen, Brady, Cody, and Diane are sharing a cake valued at $20 using the lone-divider method. The divider divides the cake into four slices \(\left(s_{1}, s_{2}, s_{3}, \text { and } s_{4}\right)\). Table 21 shows the values of the slices in the eyes of each player.
(a) Who was the divider?
(b) Find a fair division of the cake.
\(\begin{array}{|c|c|c|c|c|} \hline & \boldsymbol{s}_{1} & \boldsymbol{s}_{2} & \boldsymbol{s}_{3} & \boldsymbol{s}_{4} \\ \hline \text { Allen } & \$ 4.00 & \$ 5.00 & \$ 4.00 & \$ 7.00 \\ \hline \text { Brady } & \$ 6.00 & \$ 6.50 & \$ 4.00 & \$ 3.50 \\ \hline \text { Cody } & \$ 5.00 & \$ 5.00 & \$ 5.00 & \$ 5.00 \\ \hline \text { Diane } & \$ 7.00 & \$ 4.50 & \$ 4.00 & \$ 4.50 \\ \hline \end{array}\)
TABLE 21Questions & Answers
QUESTION:
Allen, Brady, Cody, and Diane are sharing a cake valued at $20 using the lone-divider method. The divider divides the cake into four slices \(\left(s_{1}, s_{2}, s_{3}, \text { and } s_{4}\right)\). Table 21 shows the values of the slices in the eyes of each player.
(a) Who was the divider?
(b) Find a fair division of the cake.
\(\begin{array}{|c|c|c|c|c|} \hline & \boldsymbol{s}_{1} & \boldsymbol{s}_{2} & \boldsymbol{s}_{3} & \boldsymbol{s}_{4} \\ \hline \text { Allen } & \$ 4.00 & \$ 5.00 & \$ 4.00 & \$ 7.00 \\ \hline \text { Brady } & \$ 6.00 & \$ 6.50 & \$ 4.00 & \$ 3.50 \\ \hline \text { Cody } & \$ 5.00 & \$ 5.00 & \$ 5.00 & \$ 5.00 \\ \hline \text { Diane } & \$ 7.00 & \$ 4.50 & \$ 4.00 & \$ 4.50 \\ \hline \end{array}\)
TABLE 21 ANSWER:
Step 1 of 2
The cake is valued at $20
The table given is:
\(\begin{array}{|c|c|c|c|c|} \hline & \boldsymbol{s}_{1} & \boldsymbol{s}_{2} & \boldsymbol{s}_{3} & \boldsymbol{s}_{4} \\ \hline \text { Allen } & \$ 4.00 & \$ 5.00 & \$ 4.00 & \$ 7.00 \\ \hline \text { Brady } & \$ 6.00 & \$ 6.50 & \$ 4.00 & \$ 3.50 \\ \hline \text { Cody } & \$ 5.00 & \$ 5.00 & \$ 5.00 & \$ 5.00 \\ \hline \text { Diane } & \$ 7.00 & \$ 4.50 & \$ 4.00 & \$ 4.50 \\ \hline \end{array}\)
(a) It is clear from the table that Cody is the divider. As he divides the cake into four equal shares.