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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.
Points in s2 divided by points in the whole sandwich gives the value, as a
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 Spring '07
 Berkowitz
 Math

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