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Mathematics LibreTexts

18.4: Fair Division

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    34292
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    1. Chance values the veggie half at $7.50 and pepperoni half at $2.50.

    A full pepperoni slice is \(\frac{1}{4}\) of the pepperoni half. Value \(\$ 2.50 / 4=\$ 0.625\)

    A full veggie slice is \(\frac{1}{4}\) of the veggie half. Value \(\$ 7.50 / 4=\$ 1.875\)

    A slice that is ½ pepperoni \(\frac{1}{2}\) veggie is value \(\$ 0.3125+\$ 0.9375=\$ 1.25\)

    3. Erin: Bowl 1, Catherine: Bowl 2, Shannon: Bowl 3

    5. a. 25 Snickers @ $0.01 each, 20 Milky Ways @ $0.05 each, 60 Reese’s @ $0.02 each

    Value: \(\$ 0.25+\$ 1.00+\$ 1.20=\$ 2.45\)

    b. No. Dustin values the whole bag at $8, so a fair share would be $4.

    c. Lots of possibilities. Here’s a couple:

    80 Milky Ways, 0 Snickers, 0 Reese’s

    50 Snickers, 50 Milky Ways, 50 Reese’s

    7. a. Zoe

    b. Maggie: s2, s3. Meredith: s1, s2. Holly: s3

    c. Maggie: s2, Meredith: s1, Holly: s3, Zoe: s4

    9. a. P5

    b. $6.50 (doesn’t need to trim it much since they’re last)

    c. P4 would receive it, with value $6.00 (since P4 would trim it)

    11. a. \((320+220) / 4=\$ 135\)

    b. Desk and Vanity both go to A. A pays \(\$ 320+\$ 220-\$ 135=\$ 405\) to estate

    B gets $95, C gets $125, D gets $110.

    c. Surplus of \(\$ 405-\$ 95-\$ 125-\$ 110=\$ 75\) gets split, $18.75 each.

    A gets desk and vanity, pays $386.25 to estate

    B gets $113.75, C gets $143.75, D gets $128.75

    13. Fair shares: Abby: 10.333, Ben: 9, Carla: 7.667

    Motorcycle to Abby, Car to Ben, Tractor to Abby, Boat to Abby

    Initial: Abby pays $10.667, Ben pays $2, Carla gets $7.667

    Surplus: $5; $1.667 each

    Final: Abby gets Motorcycle, Tractor and Boat, pays $9

    Ben gets Car, pays $0.333

    Carla gets $9.334

    15. Fair shares: Sasha: $135, Megan: $140

    Sasha gets: Couch, detail cleaning. Value $80

    Megan gets: TV, Stereo, carpets. Value: $260

    Initial: Sasha gets $55, Megan pays $120.

    Surplus: $65; $32.50 each

    Final: Sasha gets Couch and does detail cleaning, gets $87.50

    Megan gets TV and stereo, and cleans carpets, pays $87.50

    17. a. s3, worth $270

    b. s1 and s4 have combined value $440 for Greedy, so piece would be worth $220


    18.4: Fair Division is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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