Discrete Math Review Chapter 3. Multiple Choice Choose the one alternative that best completes the statement or answers the question.

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1 Discrete Math Review Chapter 3 Name Multiple Choice Choose the one alternative that best completes the statement or answers the question. Angela and Ben want to divide fairly the chocolate-strawberry cake shown below using the divider-chooser method. The total cost of the cake was $6.00. Angela values strawberry three times as much as she values chocolate, while Ben values chocolate twice as much as he values strawberry. a 1. In Ben s eyes, the piece shown to the right is worth A. $5.00 B. $4.00 C. $4.50 D. $4.75 c 2. In Angela s eyes, the piece shown to the right is worth A. $4.50 B. $5.00 C. $3.75 D. $2.25 a 3. In Ben s eyes, the piece shown to the right is worth A. $3.50 B. $3.00 C. $4.00 D. $2.50 d 4. In Angela s eyes, the piece show to the right is worth A. $3.75 B. $3.00 C. $3.50 D. $2.25

2 Four heirs (A, B, C, and D) must fairly divide an estate consisting of two items a house and a cabin using the method of sealed bids. The players bids (in dollars) are: A B C D House 195, , , ,000 Cabin 45,000 36,000 35,000 42,000 d 5. The original fair share of player A is worth A. $1210,000 B. $240,000 C. $80,000 D. $60,000 c 6. In the initial allocation, player A A. gets the house and an additional $55,000 from the estate B. gets the cabin and pays the estate $15,000 C. gets the cabin and an additional $15,000 from the estate D. gets the house and pays the estate $135,000 a 7. In the initial allocation, player B A. gets the house and pays the estate $150,000 B. gets $62,000 from the estate C. gets the house and the cabin and pays the estate $186,000 D. gets the house and pays the estate $274,000 d 8. After the initial allocation to each player is made, there is a surplus of A. $150,000 B. $0 C. $32,000 D. $20,000 _c 9. After all is said and done, the final allocation to player A is A. $65,000 in cash B. the cabin plus $5,000 in cash C. the cabin plus $20,000 in cash D. the cabin plus $10,000 in cash

3 Four players (A, B, C, and D) agree to divide the 12 items below using the method of markers. The players bids are as indicated. _e 10. Item 5 A. goes to C B. goes to A C. goes to D D. is left over E. goes to B c 11. Item 8 A. goes to A B. goes to B C. goes to C D. goes to D E. is left over _e 12. Item 11 A. goes to A B. goes to B C. goes to C D. goes to D E. is left over Free Response: Show all work for credit A 1 C 1 D 1 B 1 B 2 A 2 C 2 D 2 B 3 C 3 A 3 D Molly buys a chocolate strawberry vanilla cake for $ Molly values strawberry twice as much as chocolate and values chocolate twice as much as vanilla. a) Find the value of each flavor. V: $1.60 C: $3.20 S: $6.40 b) If the cake is cut into six 60 0 wedges shown in the picture, find the value of each piece. P1: $0.80 P2: $2 P3: $3.20 P4: $2.4 P5: $1.6 P6: $1.20

4 14. Three players (Minnie, Mickey, Donald) must divide a cake among themselves. Suppose the cake is divided into three slices: ( s 1 s 2 s 3 ). The following table shows the percentage of value of the entire cake that each slice represents to each player. Minnie S2, S3 whole cake s 1 s 2 s 3 Minnie $12.00 $3.00 $5.00 $4.00 Mickey $15.00 $4.00 $4.50 $6.50 Donald $13.50 $4.50 $4.50 $4.50 Mickey S3 S1 Donald S2 Minnie S3 Mickey Donald S1, S2, S3 15. Three players (Alex, Betty, and Cindy) must divide a cake among themselves. Suppose the cake is divided into three slices: ( s 1 s 2 s 3 ). The following table shows the percentage of value of the entire cake that each slice represents to each player. For each player, indicate which of the slices are fair shares. s 1 s 2 s 3 Alex 30% 40% 30% Betty 35% 25% 40% Cindy 33 1/3 % 50% 16 2/3% Alex S2 S1- Cindy, S2 Alex, S3 - Betty Betty S1, S3 Cindy S1, S2 16. Five players (Addie, Ben, Callie, Dave, and Erin) must divide a cake among themselves. Suppose the cake is divided into 5 slices (s 1, s 2, s 3, s 4, s 5 ). The value of the entire cake and of each of the five slices in the eyes of the players is shown in the table below. For each player, indicate which of the slices are fair shares. whole cake s 1 s 2 s 3 s 4 s 5 Addie $15.00 $3.25 $2.50 $3.50 $2.50 $3.25 Ben $18.00 $4.00 $4.25 $3.25 $3.75 $2.75 Callie $12.00 $2.40 $2.40 $2.40 $2.40 $2.40 Dave $10.00 $2.50 $1.75 $1.50 $2.25 $2.00 Erin $20.00 $3.50 $3.75 $5.00 $4.90 $2.85 Addie S1, S3, S5 Ben S1, S2, S4 Callie S1, S2, S3, S4, S5 Dave S1, S4, S5 Erin S3, S4

5 17. Determine a fair allocation of assets Cailey Ryan Jason Priscilla Coffee Maker Waffle Iron Quesadilla Maker Total: Fair Share: a) Determine a fair initial allocation of the items Cailey coffee maker owe 6.25 Ryan Waffle maker owe Jason Quesadilla maker owe Priscilla - receive 25 b) Determine the surplus funds is surplus everybody receive extra $9.38 c) Determine the final allocation of assets Cailey coffee maker receive 2.76 Ryan Waffle maker owe Jason Quesadilla maker owe Priscilla - receive Ana, Billy, and Cara are dividing four pieces of furniture using the method of sealed bids. Their bids on each of the items are given in the following table. Ana Billy Cara Dresser $150 $300 $275 Desk $180 $150 $165 Vanity $170 $200 $260 Tapestry $400 $250 $500 a) Determine a fair initial allocation of the items Ana desk receive 120 Billy dresser Cara vanity and tapestry owe 360 b) Determine the surplus funds 240 and everybody receives an extra 80 c) Determine the final allocation of assets Ana desk receive 20 Billy dresser receive 80 Cara vanity and tapestry owe 280

6 19. Determine a fair allocation of assets 20. Johnathan Joe Billy Jeremy Car 25,000 32,000 41,000 27,000 House 150, , , ,000 Painting 1, Total: Fair Share: a) Determine a fair initial allocation of the items Johnathan painting receive Joe house owe Billy car receive Jeremy - receive b) Determine the surplus funds everybody receives c) Determine the final allocation of assets Johnathan painting receive Joe house owe Billy car receive Jeremy - receive Determine the allocation of candy to each player: A: Which items are left over? 5, 6, 10, 11 B: 1-4 C: 7-9 D: Three children (A, B, and C) are dividing the array of 12 candy pieces show in the following figure using the method of markers. The players bids are indicated in the figure A 1 C 1 A 2 B 2 a. Describe the allocation of candy to each child. B 1 C 2 A 1, 2 B C 4 9 b. Which items are left over? 3, 8, 9