I. (Use this information for problems 1-12.)
Al, Ben, and Carl decide to ‘fairly divide’ a $3.96 box of doughnuts (9 are
CHOCOLATE, 12 are CREME FILLED, and 12 are PLAIN).
Al likes the PLAIN ones but hates the others; Ben likes all three types equally well; and
Carl hates the CHOCOLATE ones, likes the PLAIN ones but likes the CREME FILLED ones twice
as much as the PLAIN ones.
1. How much would Al decide the 9 CHOCOLATE ones are worth (to him)?
2. How much would Al decide the 12 CREME FILLED ones are worth (to him)?
3. How much would A1 decide the 12 PLAIN ones are worth (to him)?
4. How much would Ben decide the 9 CHOCOLATE ones are worth (to him)?
5. How much would Ben decide the 12 CREME FILLED
ones are worth (to him)?
6. How much would Ben decide the 12 PLAIN ones are worth (to him)?
7. How much would Carl decide the 9 CHOCOLATE ones ones are worth (to him)?
8. How much would Carl decide the 12 CREME FILLED ones are worth (to him)?
9. How much would Carl decide the 12 PLAIN ones are worth (to him)?
10. If Al had to ‘fairly divide’ these doughnuts into 3 shares of equal value (to him), how might he do it? Is there more than one way? If so, show another.
11. If Ben had to ‘fairly divide’ these doughnuts into 3 shares of equal value (to him), how might he do it? Is there more than one way? If so, show another.
12. If Carl had to ‘fairly divide’
these doughnuts into 3 shares of equal value (to him), how might he do it? Is there more
than one way? If so, show another.
II. (Use this information for problems 13-14.)
A tract of land consists of 3 distinct
sections: Agricultural, Forest, and Residential. The relative size of each section is
represented by the figure below.
13. Five years ago, the entire tract was worth a
total of $750,000, Agricultural and Residential land was equally valuable and was twice as
valuable as Forest. How much was each of the 3 sections of land worth five years ago?
14. Today, the entire tract is worth a total of $770,000. However, now Agricultural land is worth twice as much as Forest and Forest is twice as valuable as Residential. How much is each of the 3 sections of land worth today?