3. A team triathlon consists of a 16-mile run, an 80-mile bike ride, and a 9-mile swim. A team consists of three members. Matt’s running-to-biking-to-swimming ratio is 1 to 4 to 1. Jory’s ratios is 2 to 2 to 1 and Sart’s ratio is 3 to 1 to 4. The events will be divided according to the divide –and-choose method for three players.
b) Would a 3-mile run, a 10-mile ride, and a 4-mile swim be considered a fair share by any of the three teammates? Justify your answer. (Hint: calculate how many pts this division would equal for each of the 3 players and then compare to your chart above.)
4. Three kids, Holly, Harvey, and Hanna, must share a candy bar. For each of the following scenarios, describe the steps in a fair division of the candy bar using the last-diminisher method.
Holly makes the first cut. Harvey feels the portion is less than a fair share, so he does not make any cuts. Hanna also feels the portion is less than a fair share, so she does not make any cuts. How does this scenario proceed to an end?
Holly gets first piece (one she cut. The last person to cut gets his/her piece.) Harvey and Hanna use the divide and choose method.
b) Holly makes the first cut. Harvey feels the portion is less than a fair share, so he does not make any cuts. Hanna thinks the portion is too big, so she trims the piece. What happens next and how could this scenario end?
Hanna gets the portion she trimmed. The trimmings are combined with the rest of the candy bar. Holly and Harvey divide and choose.
5. Twins Else and Emma receive a painting from their grandmother. Both girls admired the painting often, and the grandmother could not decide which one to give it to. Else believes the painting is worth $780 and Emma feels it is worth $835. The girls both want the painting, but they agree to use the method of sealed bids to help them create a fair division. What is the result of the division? Show all work.
6. A couple, Maxine and Dugan, are parting ways and must figure out a way to split up their belongings, including an antique chair, a plasma television, a patio set, a treadmill, and a lawnmower. They agree to abide by the result of the method of sealed bids. Each makes the following bids on each item.