Honors Discrete Chapter 3 Review: SOLUTIONS

Find the Value Fractions for the following people:

  1. Geoff likes chocolate ice cream twice as much as vanilla.

CHOCOALTE = 2/3VANILLA = 1/3

  1. Joy likes peanut butter 3 times as much as she likes jelly, but she likes jam twice as much as jelly.

PB = 3/6JELLY = 1/6JAM = 2/6

  1. Georgia likes pound cake 4 times as much as she likes angel food cake, and likes carrot cake twice as much as angel food cake.

PC = 4/7AFC = 1/7CC = 2/7

  1. Michael likes mocha 3 times as much as tea, and likes iced coffee twice as much as mocha.

MOCHA = 3/10TEA = 1/10ICED COFFEE = 6/10

Calculate the value of the following shares to each person:

  1. Greg likes red velvet cake 3 times as much as cookie cake.

Piece #1: 900 Red Velvet and 700 cookie

¾(90/180) + ¼ (70/180) = 15/36

Piece #2: 1100 Cookie and 300 Red Velvet.

¾(30/180) + ¼ (110/180) = 5/18

Piece #3: 600 Red Velvet

¾(60/180) = ¼

  1. Jessica likes both Mint Chocolate Chip and Cookies and Cream ice cream twice as much as vanilla and hates strawberry. Quinten likes strawberry twice as much as all other flavors.

Jessica: MCC =2/5 CC = 2/5 V = 1/5 S = 0Quinten: S = 2/5MCC = CC = V = 1/5

Piece #1: 900 Vanilla and 450 Mint Chocolate Chip

Jessica: 1/5(90/90) + 2/5(45/90) = .4

Quinten:1/5(90/90) + 1/5(45/90) = .3

Piece #2: 450 Mint Chocolate Chip and 600 Strawberry

Jessica:2/5(45/90) + 0(60/90) = .2

Quinten:1/5(45/90) + 2/5(60/90) = 11/30

Piece #3: 300 Strawberry and 900 Cookies and Cream

Jessica:0(30/90) + 2/5(90/90) = 2/5

Quinten:2/5(30/90) + 1/5(90/90) = 1/3

LONE-DIVIDER METHOD:

#1 / S1 / S2 / S3
P1 / 30% / 40% / 30%
P2 / 331/3% / 331/3% / 331/3%
P3 / 50% / 15% / 35%

A. Who is the divider?P2

B. What is the bid list of each player?

P1 = {S2}, P2 = All, P3 = { S1, S3}

C. What is the fair division of the shares?

P1 = S2P2 = S3P3 = S1

#2 / S1 / S2 / S3 / S4
P1 / 45% / 35% / 10% / 10%
P2 / 25% / 20% / 20% / 35%
P3 / 0% / 50% / 40% / 10%
P4 / 25% / 25% / 25% / 25%

A. Who is the divider?P4

B. What is the bid list of each player?

P1 = {S1, S2}, P2 = {S1, S4}, P3 = {S2, S3},
P4= All

C. What is the fair division of the shares?

P1 = S1P2 = S4P3 = S2P4 = S3

#3 / S1 / S2 / S3 / S4 / S5
P1 / 10% / 40% / 7% / 35% / 8%
P2 / 25% / 10% / 35% / 15% / 15%
P3 / 20% / 20% / 20% / 20% / 20%
P4 / 30% / 15% / 22% / 13% / 20%
P5 / 5% / 30% / 15% / 35% / 15%

A. Who is the divider?P3

B. What is the bid list of each player?

P1 = {S2, S4}, P2 = {S1, S3},
P3 =All, P4 = {S1, S3, S5}, P5 = {S2, S4}

C. What is the fair division of the shares?P1 = S2P2 = S3P3 = S1P4 = S5 P4 = S4

Perform the Method of Markers: Marks will be given

one option: answers will vary

ABCDABBABCCDDBD

Perform the Method of Sealed Bids:

P1 / P2 / P3 / P4
House / 250,000 / 300,000 / 350,000 / 400,000
Car / 120,000 / 115,000 / 115,000 / 110,000
Boat / 280,000 / 270,000 / 295,000 / 275,000
Painting / 25,000 / 35,000 / 30,000 / 25,000
Cabin / 115,000 / 113,000 / 117,000 / 116,000
FDS / 197,500 / 208,250 / 226,750 / 231,500
Owe/Owed / Get 77,500 / Get 173,250 / Pay 185,250 / Pay 168,500
Surplus / (185,250 + 168,500 – 77500 – 173250)/4 = 25,750
Final / Car and Get 103,250 / Painting Get 199,000 / Boat/ Cabin and Pay 159,500 / House and Pay 142,750

Chapter 3 Fair Division Practice Multiple Choice

For Questions #1 – 3: Three players agree to split jolly ranchers using the method of markers. The marks for the 3 players are shown below.

ACCWAAGWGBABWCB

1) According to player one which of the following isn’t a fair amount of jolly ranchers?

A) ACCWAB) ACCWC) AGWGBD) ABWCBE) All

2) Which of following is the correct allocation of jolly ranchers?

A) P1 = 1st Segment, P2 = 2nd Segment, P3 = 3rd Segment

B) P1 = 3rd Segment, P2 = 2nd Segment, P3 = 1st Segment

C) P1 = 3rd Segment, P2 = 1st Segment, P3 = 2nd Segment

D) P1 = 2nd Segment, P2 = 1st Segment, P3 = 3rd Segment

E) None of the Above

3) Which of the following is the leftover for the method?

A) AB) A, AC) W, GD) B, W, C, BE) No Leftovers

Use the following to answer questions #4 - #8: Method of Sealed Bids.

Player A / Player B / Player C
Item #1 / 1380 / 1200 / 1000
Item #2 / 720 / 500 / 725
Item #3 / 900 / 1000 / 750

4) Who will receive the Item #1?

a) Ab) Bc) Cd) All playerse) No one.

5) What is the fair dollar share for Player B?

a) 1200b) 825c) 900d) 1000e) 2700

6) In the first settlement, how much money will Player C get?

a) 725b) 2475c) 825d) 100e) None of the above

7) What is the total surplus?

a) 100b) 126.66c) 380d) 480 e) None of the above

8) Which of the following describes Player A’s final settlement?

a) Item #1 and Item #2, Pay 380 and Get 126.66

b) Item #2, Get 280, Get 126.66

c) Item #1, Pay 380 and Get 126.66

d) Item #3, Get 100 and Get 126.66

e) None of the above