class+March1 - Math 103 Section 11 Tuesday March 1 2011...

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Math 103, Section 11, Tuesday, March 1, 2011 Chapter 3 Handout 3 Exam # 1 on Friday, March 4 covering Chapters 1,2 and 4. The Mathematics of Sharing Assignment Chapter 3A Please do Exercises 12,18,30, and 32, pages 105-109 and upload to Sakai. Homework is due by Tuesday, March 8, 5 minutes before midnight Assignment Chapter 3B Please do Exercises 42, 56, and 70. Homework to be discussed in class on Tuesday, March 8. Lone-divider problems: Exercises 23 and 31,.#31 answers a question that Roberta asked! Lone-chooser: Exercise 41. Divider-chooser method; 17.
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Solution to problem #17 a. Again, we use the point system. Let 1 point =the value of 1 inch of turkey sub to Martha. Then 1 point=the value of 1 inch of roast beef sub and 2 points=the value of 1 inch of ham sub to Martha. To Martha, the whole sandwich has a point value=8*2+20*1=36 points. So Martha will cut the sandwich as the 18 point mark. Where is this mark? The ham section is 2*8=16 points. We need 2 more points. This is 2 inches of turkey. So Martha cuts at the 10 inch mark. S1=[0,10] and s2=[10,28]. b. b. The value of s1 to Nick is 10 points and the value of s2 to Nick is 10*1 point+8*2 points=26 points. So Nick will choose s2 with 26 points. The value to Nick of the whole sandwich is 20*1 point+8*2 points =36 points. The value of his piece is 26/36 * $9=26/4=$ 6.50 Dear Students, Here is a method for solving sandwich problems that will always work: 1. Start with the divider: Let 1 point equal the value of 1 inch of the piece of least value. (If it has zero value, then instead of 1 point use 0 points. For example, Karla is a vegetarian. The value of 1 inch of meatball sub is 0 points. For Karla, the value of 1 inch of vegetarian sub is 1 point.) Then add up the total value in points for the divider. Call it T for total. Find T/2. That is the number of points that will be to the left of the knife and the number of points that will be to the right of the knife. That is, the divider is making the value equal on the left of the cut and on the right of the cut. 2. Find the actual spot on the ruler where this cut needs to be made. That is, find where T/2 corresponds on the ruler. You “count off” points. 3. Make the cut. Then the divider has made the value of s1=50% and the value of s2=50% or 50% of the cost of the whole sandwich. 4. Now for the chooser: Calculate how many points are in the whole sandwich, how many points are in s1 and how many points are in s2. Points in s1 divided by points in the whole sandwich gives the value, as a fraction, of s1 to the chooser. If you multiply this fraction by the cost of the whole sandwich, you get the value, in money, of the piece, s1, to the chooser.
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Points in s2 divided by points in the whole sandwich gives the value, as a fraction, of s2 to the chooser. If you multiply this fraction by the cost of the whole sandwich, you get the value, in money, of the piece, s2, to the chooser.
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