Any assistance with the following Divider - Chooser Method Question would be hel

Question

Any assistance with the following Divider - Chooser Method Question would be helpful;

Kyle and Maria are planning to share a pizza that is three equal parts pepperoni, sausage, and mushroom. Kyle likes pepperoni and sausage equally, and he likes sausage twice as much as mushroom. Maria likes sausage and mushroom equally well, but hates pepperoni.

1) Where would Kyle cut the pizza for equal shares? (S1/S2)

2) What share would Maria choose?

3) What is the value in percent(%) to Maria?

4) Where would Maria cut the pizza for equal shares? (S1/S2)

5) What share would Kyle choose?

6) What is the value in percent(%) to Kyle?

Explanation / Answer

Let us assume the value of pizza to be $9

Kyle likes pepperoni and sausage equally, and he likes sausage twice as much as the mushroom.

let the value of sausage be x

Since he equally likes pepperoni so the value of pepperoni = x

and he likes mushroom half as sausage, the value of mushroom = x/2

x + x + x/2 = 9

x = $18/5

Sausage and pepperoni is worth $18/5 (40%) to Kyle and mushrooms $9/5 (20%)

Maria likes sausage and mushroom equally well but hates pepperoni.

Pepperoni is worthless to her since she hates it

2x = 9

So sausage and mushroom are equally worth $9/2 (50%)

The table depicts value of each type of pizza to Kyle and Maria

1) Where would Kyle cut the pizza for equal shares? (S1/S2)

Divider = Kyle

Assumption: Kyle must be unaware of maria's preferences

9 slices of pizza 3 of each sausage, pepperoni, and mushroom

Kyle would cut the pizza in following way which according to him is equal share of 50%

S1: One-half pizza = 3 slices sausage and 1.5 slices mushroom = 40% + 10% = 50%

S2: 2nd half pizza = 3 slices of pepperoni and 1.5 slices of mushroom = 40% + 10% = 50%

2) Since Maria dislikes pepperoni she will choose S1 which contains sausage and mushroom

3) Maria's value of S1 = (3 slices of sausage) 50% + (1.5 slices slices of mushroom) 25% = 75%

4) Maria cut for the equal share

S1: 3 slices of sausage + 1.5 slices of pepperoni = 50% + 0% = 50%

S2: 3 slices of mushroom + 1.5 slices of pepperoni = 50% + 0% = 50%

5) Since kyle like sausage twice more than mushroom, he will choose S1

6) Kyle's value for S1 : 3 slices of sausage (40%) + 1.5 slices of pepperoni (20%) = 60%

Sausage (3 slices) Mushroom(3 slices) Pepperoni(3 slices) Kyle 40% 20% 40% Maria 50% 50% 0%

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