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Excursions in Modern Mathematics: Pearson New International Edition | 8th Edition | ISBN: 9781292022048 | Authors: Peter Tannenbaum
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Angelina and Brad jointly buy the chocolate-strawberry mousse cake shown in Fig. 18(a)

Chapter 3, Problem 11

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QUESTION:

Angelina and Brad jointly buy the chocolate-strawberry mousse cake shown in Fig. 18(a) for $36. Suppose that Angelina values chocolate cake twice as much as she values strawberry cake. Find the dollar value to Angelina of each of the following pieces of cake: (a) the strawberry half of the cake (b) the chocolate half of the cake (c) the slice of strawberry cake shown in Fig. 18(b) (d) the slice of chocolate cake shown in Fig. 18(c)

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QUESTION:

Angelina and Brad jointly buy the chocolate-strawberry mousse cake shown in Fig. 18(a) for $36. Suppose that Angelina values chocolate cake twice as much as she values strawberry cake. Find the dollar value to Angelina of each of the following pieces of cake: (a) the strawberry half of the cake (b) the chocolate half of the cake (c) the slice of strawberry cake shown in Fig. 18(b) (d) the slice of chocolate cake shown in Fig. 18(c)

ANSWER:

Step 1 of 4

(a)

Use Fair Division Games in which objects are divided in positive or negative value and players jointly own the assets and divide the object among themselves.

Consider Angelina and Brad jointly buy chocolate-strawberry mousse cake the value of whole cake is  is equal to .

Divide the cake in two halves, one half chocolate cake as  and other half strawberry as .

By fair division Angelina values chocolate cake twice as much as she values strawberry cakes in ratio written as  thus, in the value of  strawberry cake is:

Therefore, the value of the strawberry half of the cake is .

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