Fair Division

# Fair Division

## Fair Division

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##### Presentation Transcript

1. Fair Division The Value of a Slice

2. Value of a Slice T. Serino Briana likes strawberry cake twice as much as she likes vanilla. If the following half vanilla, half strawberry cake is worth \$12, determine the value of each half of the cake using Briana's value system. vanilla strawberry

3. Value of a Slice T. Serino 3 equal slices according to Briana’s value system. The vanilla half of the cake is worth 1/3 of the whole cake according to Brianna’s value system. (1 out of 3 equal pieces is vanilla) of the whole cake is vanilla The whole vanilla half of the cake is worth \$4 to Brianna.

4. Value of a Slice T. Serino 3 equal slices according to Briana’s value system. The strawberry half of the cake is worth 2/3 of the whole cake according to Brianna’s value system. (2 out of 3 equal pieces are strawberry) of the whole cake is strawberry The whole strawberry half of the cake is worth \$8 to Brianna.

5. Value of a Slice T. Serino Briana likes strawberry cake twice as much as she likes vanilla. If the following half vanilla, half strawberry cake is worth \$12, determine the value of the following slice of the cake using Briana's value system. part whole Remember: Whole strawberry half is worth \$8 Whole vanilla half is worth \$4 Vanilla: of the whole vanilla half The 90o piece of vanilla is worth \$2 to Brianna.

6. Value of a Slice T. Serino Briana likes strawberry cake twice as much as she likes vanilla. If the following half vanilla, half strawberry cake is worth \$12, determine the value of the following slice of the cake using Briana's value system. Strawberry part whole Whole vanilla half is worth \$4 Whole strawberry half is worth \$8 of the whole strawberry half The 45o piece of strawberry is worth \$2 to Brianna.

7. Value of a Slice T. Serino Briana likes strawberry cake twice as much as she likes vanilla. If the following half vanilla, half strawberry cake is worth \$12, determine the value of the following slice of the cake using Briana's value system. The 45o piece of strawberry is worth \$2 to Brianna. The 90o piece of vanilla is worth \$2 to Brianna. \$2 \$2 \$4.00 The whole piece of cake is worth \$2+\$2

8. Value of a Slice T. Serino Raquel likes strawberry cake twice as much as she likes vanilla and she likes chocolate and vanilla equally. If the following vanilla, strawberry, chocolate cake is worth \$36, determine the value of each third of the cake using Raquel's value system. Strawberry Chocolate Vanilla

9. Value of a Slice T. Serino \$36 cake Chocolate Strawberry 1 of 4 equal slices 2 of 4 equal slices \$9.00 \$18.00 Vanilla 1 of 4 equal slices \$9.00

10. Value of a Slice T. Serino Raquel likes strawberry cake twice as much as she likes vanilla and she likes chocolate and vanilla equally. If the following vanilla, strawberry, chocolate cake is worth \$36, determine the value of slice s1 and s2 using Briana's value system. s1 s2 s1 s2

11. Value of a Slice T. Serino s1 s2 \$18 \$9 s1 \$9 S1 is worth \$6.75 according to Raquel’s value system.

12. Value of a Slice T. Serino s1 s2 \$18 \$9 \$9 s2 S2 is worth \$6.75 according to Raquel’s value system.

13. Try this. T. Serino Anthony likes vanilla cake three times as much as he likes strawberry. If the following half vanilla, half strawberry cake is worth \$20, answer the following. What is the value of the whole vanilla half of the cake according to Anthony’s value system? What is the value of the whole strawberry half of the cake according to Anthony’s value system? c) What is the value of the slice shown according to Anthony’s value system? Solutions a) \$15 b) \$5 45o 30o c) \$3.75

14. M athematical D ecision M aking