1. Fair Division
The Value of a Slice

2. Value of a Slice vanilla strawberry
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.
strawberry
vanilla

3. Value of a Slice
T. Serino
First divide the cake into equal slices according to Briana’s value system. (3 Equal slices in this case)
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 3 equal slices according to Briana’s value system.
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 part whole
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. (Hint: find the value of each flavor separately.)
Remember:
Whole vanilla half is worth $4
Whole strawberry half is worth $8
Vanilla:
part
whole
of the whole vanilla half
The 90o piece of vanilla is worth $2 to Brianna.

6. Value of a Slice part whole
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
Whole vanilla half is worth $4
Whole strawberry half is worth $8
part
whole
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. $2
The 90o piece of vanilla is worth $2 to Brianna. $2
$2+$2
$4.00
The whole piece of cake is worth

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.
Four equal slices according to Raquel’s value system.
Strawberry
Chocolate
Vanilla
Note that the angle of each flavored sector here is 120o.

9. Value of a Slice $36 cake Chocolate Strawberry Vanilla
T. Serino
$36 cake
Chocolate
Strawberry
1 of 4 equal slices
$9.00
2 of 4 equal slices
$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 s2 s1

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

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

13. Try this. Solutions a) $15 b) $5 c) $3.75
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. (Show work!)
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
c) $3.75
45o
30o

14. athematical M D
ecision
aking