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Dustin and Quinn were given an apple pie and a chocolate cake, and need to divide them. Dustin values the apple pie at $6 and the chocolate cake at $4. Quinn values the apple pie as $4 and the chocolate cake at $10. Describe a fair division if Quinn is dividing in a way that one "half" will be exclusively chocolate, and specify which "half" Dustin will choose.

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Answer:

Quinn values the apple pie at $4 and the chocolate cake at $10 = total $14

  1. since one "half" will only be chocolate, he needs $7 out of chocolate = 7/10 of the chocolate cake.
  2. the other "half" will include 3/10 of chocolate cake and the whole apple pie = (3/10 x $10) + $4 = $3 + $4 = $7

If Dustin chooses the second "half" he will receive 3/10 of chocolate cake and the whole apple pie = (3/10 x $4) + $6 = $1.20 + $6 = $7.20

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