Chapter+3+Takehome+Quizsolutions

# Chapter+3+Takehome+Quizsolutions - Math 103 Section 11...

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Math 103 Section 11 Take-home Quiz for Chapter 3 3/11/11 Name____________________ You may use your notes or ask me questions. Assignment is due on Friday, March 25, 2011 5 points 1. Four friends (Joe, Tim, Sam, and Ron) have decided to divide up a multi-flavored cake which was jointly purchased for \$24 using the Lone-Divider Method . The cake is divided into four pieces { s 1, s 2 , s 3 , and s 4} . The following table gives the dollar value of each of the slices according to each of the four friends. Friend s1 s2 s3 s4 Fair share value Fair shares Joe \$8.00 \$7.00 \$4.00 \$5.00 (8+7+4+5)/4=\$6 s1,s2 Tim \$6.00 \$6.00 \$6.00 \$6.00 \$6. s1,s2,s3,s4 Sam \$5.50 \$10.00 \$4.50 \$4.00 (5.50+10+4.50+4)/4=\$6 s2 Ron \$5.50 \$9.00 \$3.50 \$6.00 (5.50+9+3.50+6)/4=\$6 s2,s4 a. Complete the above table. Note that the fair share value is \$6 for each of the friends as each of their four bids add up to the value of the cake, \$24. b. Which of the four friends is the divider ? Tim How do you know this? All the shares have the same value c. Find a fair division of the cake and explain why this is the only possible fair division. Sam must get s2. Then Joe must get s1. Ron must get s4. Tim gets the last piece, s3.

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2. 10 points Martha and Nick jointly bought the giant 28 inch sub sandwich shown above for \$16. They plan to divide the sandwich fairly using the divider- chooser method. Martha likes ham subs twice as much as she likes turkey subs and she likes roast beef subs three times as much as she likes turkey subs. Nick likes turkey subs twice as much as he likes ham subs and he likes roast beef subs four times as much as he likes ham subs. They flip a coin and Martha ends up being the divider.
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## This note was uploaded on 01/20/2012 for the course MATH 103 taught by Professor Berkowitz during the Spring '07 term at Rutgers.

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Chapter+3+Takehome+Quizsolutions - Math 103 Section 11...

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