CMT: QUARTER 2 FAIR DIVISION (VALUE SYSTEMS PART 2) NOTES

Bob and Bernice are on a first date! They have bought this Black-and-White cookie and have decided to split it. Bob likes chocolate three times as much as vanilla. Bernice likes vanilla and chocolate equally. However, because it is their first date, they do not know each other’s value system.

RECALL: Complete the value table for each.

Bob Bernice

Chocolate / Vanilla
Ratio
Fraction
Percent
Chocolate / Vanilla
Ratio
Fraction
Percent

If the cake cost $16.00, what is the monetary value of the

  1. Chocolate half to Bob?
  1. Vanilla half to Bob?
  1. Chocolate half to Bernice?
  1. Vanilla half to Bernice?

Bob splits the cookie in half, making sure that each part has half chocolate and half vanilla. He asks Bernice to choose which half she would like.

  1. After Bernice chooses her piece, Bob is left with the piece below. What is Bob’s monetary value of the piece he has received?

Formula for finding the value of a circular PART:

*Add together as many flavors as are in the part.

In the introductory problem, Bob had made received a piece that was ½ of the value of the total goods. Therefore, it was a fair share. Investigate the other cuts below.

Determine Bob’s value of the other possible cuts of the Black-and-White cookie. Is the piece a fair share?

1.)

2.)

3.)Brianna is eating the mushroom-pepperoni-cheese pizza shown to the right.

  1. If the amount of mushroom, pepperoni, and cheese is equal, how many degrees are in each section? Label this number on the pizza.
  1. If Brianna likes mushroom twice as much as cheese and likes pepperoni twice as much as mushroom, what is her value of each item. Please round your percent to the nearest whole number.

Mushroom / Pepperoni / Cheese
Ratio
Fraction
Percent
  1. What is Brianna’s percent value of each slice shown below? Round your answer to one decimal place, if needed.

II.

Formula for finding the value of a rectangular PART:

*Add together as many flavors as are in the part.

4.) Jess likes strawberry four times as much as vanilla. She has paid $28.00 for a half-strawberry and half-vanilla cake that she will be bringing to a Holiday party.

  1. Determine Jess’s percent value of each side.
  1. In her eyes, how much money is the vanilla portion of the cake worth?
  1. In her eyes, how much money is the strawberry portion of the cake worth?
  1. What is the area of each side of the cake?
  1. How much would the piece to the right be worth to Jess?

5.)Andres has a Secret Santa! Yesterday during lunch, a pizza was delivered to him in the school cafeteria. Andres likes pepperoni (P) and mushroom (M) equally, but likes green peppers (G) twice as much as those. To his dismay, his Secret Santa must not know him well because Andres hates anchovies (A).

  1. Complete the value table based on Andres’s preferences.

Green Peppers / Pepperoni / Mushroom / Anchovies
Ratio
Fraction
Percent
  1. To show his appreciation, Andres eats a big slice which includes all four toppings. This slice is highlighted in the pizza below. If the area of each section of the pizza is 16 square inches, what is the percent value of the highlighted slice according to Andres?