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Math 103
Exam #2Solutions
April 19, 2011
There are 11 problems and 2 extra credit problem.
Good luck and have fun! Show me all you’ve learned !
1. 10 points
Alex, Judy, and Lois are dividing the 18 inch long sub which has a 12 inch vegetarian
piece and a 6 inch meat piece.
The sub is shown in the above picture. The three
friends are dividing the sub using the
lonechooser method
.
Alex likes the vegetarian and meatball parts equally well.
Judy likes the meatball part four times as much as she likes the vegetarian part.
Lois likes the meatball part twice as much as she likes the vegetarian part.
Alex and Judy are the dividers and Lois is the chooser.
In the first division, Judy divides
the sub into two shares (a left share s1 and a right share s2).
a. After Judy cuts, Alex gets to choose. Specify which of the two shares
Alex should choose, and give the values of the shares to Judy and Alex.
Value table
Vegetarian
Meatball
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1 point
1 point
Judy
1 point
4 point
Lois
1 point
2 points
To Judy, the whole sub is worth 1*12+4*6*=36 points
Half is 18 points. All vegetarian is 12 points. In the meat part, we need
6 points.
6 points * 1 inch/ 4 points=1.5 inches
Judy cuts at the 12+1.5 inch mark from the left.
13.5 inch mark
Put your answers in the following table:
Shares
s1=[0 ,13.5]
s2=[13.5, 18]
value to Judy (as a fraction)
½
1/2
value to Alex (as a fraction)
13.5/18
4.5/18
a. Alex chooses s1 or s2?
Alex chooses s1 since it has a larger value to him.
b. Describe how Judy would then subdivide her share into three pieces. Use interval
notation.
There are 4.5 inches of meat in
s2=[13.5, 18].
Dividing in 3 pieces, each piece is 1.5 inch.
The 3 pieces are :
[13.5,15]
[15,16.5]
[16.5,18]
c. Describe how Alex would then subdivide his share into three pieces. Use interval
notation.
s1=[0 ,13.5]
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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.
 Spring '07
 Berkowitz
 Math

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