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Solved: Suppose that Angela and Boris are the dividers and Carlos is the chooser. In the
Chapter 3, Problem 37(choose chapter or problem)
Suppose that Angela and Boris are the dividers and Carlos is the chooser. In the first division, Angela cuts the cake into two shares: s1 (a 120 strawberry-only piece) and s2 (a 60 strawberry180 vanilla piece) as shown in Fig. 26. Boris picks the share he likes best, and Angela gets the other share. In the second division, Angela subdivides her share of the cake into three pieces and Boris subdivides his share of the cake into three pieces. s2 s1 FiGuRE 25 FiGuRE 26 s1 s2 (a) Describe which share (s1 or s2) Boris picks and how he might subdivide it. (b) Describe how Angela would subdivide her share of the cake. (c) Based on the subdivisions in (a) and (b), describe a possible final fair division of the cake. (d) For the final fair division you described in (c), find the value (in dollars and cents) of each share in the eyes of the player receiving it.
Questions & Answers
QUESTION:
Suppose that Angela and Boris are the dividers and Carlos is the chooser. In the first division, Angela cuts the cake into two shares: s1 (a 120 strawberry-only piece) and s2 (a 60 strawberry180 vanilla piece) as shown in Fig. 26. Boris picks the share he likes best, and Angela gets the other share. In the second division, Angela subdivides her share of the cake into three pieces and Boris subdivides his share of the cake into three pieces. s2 s1 FiGuRE 25 FiGuRE 26 s1 s2 (a) Describe which share (s1 or s2) Boris picks and how he might subdivide it. (b) Describe how Angela would subdivide her share of the cake. (c) Based on the subdivisions in (a) and (b), describe a possible final fair division of the cake. (d) For the final fair division you described in (c), find the value (in dollars and cents) of each share in the eyes of the player receiving it.
ANSWER:Step 1 of 4
(a)
Use the Lone Chooser Method in which Angela and Boris are dividers and Carlos is the chooser.
Division: Consider whole cake as 360° . Angela divides the cake in two shares. is only strawberry piece is 120° and in 60° is strawberry and 180° vanilla piece.
In share total part is 60° + 180° = 240° and in share total part is 120°. Thus, share is double of .
Therefore, Boris pick the share as it is best.
Boris subdivides its part in three pieces as follows:
180° vanilla piece divides in two equal pieces as 90° each and 60° is strawberry.
Therefore, Boris subdivides its share as 90° vanilla, 90° vanilla and 60° strawberry.