2. Three players (Adam, Bob and Chad) are sharing a cake. Suppose that the cake is divided into three slices (s1, s2, s3). The following table shows the value of s1, and of s2 to teach of the players. The values of s3 are missing. (The percentage represent the value of the slice as a percent of the value of the entire cake)

s1 s2
Adam 30% 50%
Bob 32% 36%
Chad 30% 35%

a. Which of the three slices are fair shares to Adam?
b. Which of the three slices are fair shares to Bob?
c. Which of the three slices are fair shares to Chad?

You need to define what's "fair" here. None of the choices provides equal amounts to all three. Is any of them fair to anyone?

Maybe fairness depends on weight, or hunger, or social standing. This question is meaningless without an explanation of what's fair.

If by "fair" you mean which provides at least 1/3 of the cake to a person, then
#1 is "fair" only to whoever gets s2.

To determine which of the three slices are fair shares to each player, we need to compare the values of each slice for each player.

a. To find Adam's fair shares, we need to compare the values of s1 for Adam, Bob, and Chad. According to the table, Adam's s1 is 30%. Now we compare it to the values of s1 for Bob and Chad:

- Bob's s1 is 32%, which is greater than Adam's 30%, so it is not a fair share for Adam.
- Chad's s1 is also 30%, which is equal to Adam's 30%. This means it is a fair share for Adam.

Therefore, s1 is a fair share to Adam.

b. To find Bob's fair shares, we compare the values of s2 for Bob, Adam, and Chad. According to the table, Bob's s2 is 36%. Now we compare it to the values of s2 for Adam and Chad:

- Adam's s2 is 50%, which is greater than Bob's 36%, so it is not a fair share for Bob.
- Chad's s2 is 35%, which is less than Bob's 36%, so it is also not a fair share for Bob.

Therefore, there is no fair share to Bob.

c. To find Chad's fair shares, we compare the values of s3 for Chad, Adam, and Bob. According to the table, the values of s3 are missing. We can calculate s3 for Chad by subtracting the sum of Chad's s1 and s2 from 100%:

Chad's s3 = 100% - Chad's s1 - Chad's s2
Chad's s3 = 100% - 30% - 35%
Chad's s3 = 35%

Therefore, s3 is a fair share to Chad.

In summary:
a. s1 is a fair share to Adam.
b. There is no fair share to Bob.
c. s3 is a fair share to Chad.