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The question revolves around a fair division problem involving Dustin and Kendra who wish to split a bag of candy using the *divider-chooser* method. The bag contains three types of candy:

- 100 Snickers, which Dustin values at $0.01 each (total value = $1 for all 100 Snickers)
- 100 Milky Ways, which Dustin values at $0.05 each (total value = $5 for all 100 Milky Ways)
- 100 Reese’s, which Dustin values at $0.02 each (total value = $2 for all 100 Reese's)

The total value, according to Dustin’s valuation, is:
\[
1 + 5 + 2 = 8 \text{ dollars.}
\]

### Questions:
If Kendra is the divider and splits the candies as follows:
- 25 Snickers
- 20 Milky Ways
- 60 Reese's

The questions are:
1. **What is the value of this half in Dustin’s eyes?**
2. **Does Dustin consider this a fair share?**
3. **If Dustin was the divider, find a possible division that is consistent with his value system.**

---

### Step-by-Step Solutions

#### Part (a): Calculating the Value of the Half in Dustin’s Eyes

For this division, let's calculate how much Dustin values each type of candy in this half.

1. **Snickers**: 
   - 25 Snickers valued at $0.01 each.
   - Value = $25 \times 0.01 = 0.25$ dollars.

2. **Milky Ways**: 
   - 20 Milky Ways valued at $0.05 each.
   - Value = $20 \times 0.05 = 1.00$ dollar.

3. **Reese’s**: 
   - 60 Reese’s valued at $0.02 each.
   - Value = $60 \times 0.02 = 1.20$ dollars.

Adding these values:
\[
0.25 + 1.00 + 1.20 = 2.45 \text{ dollars.}
\]

So, **the value of this half in Dustin’s eyes is $2.45**.

#### Part (b): Determining if This is a Fair Share

Since the total value of the candy is $8 (according to Dustin), a fair share would be $4 (half of $8).

Dustin values this half at $2.45, which is significantly less than $4. Therefore, **Dustin does not consider this a fair share**.

#### Part (c): Finding a Fair Division if Dustin Were the Divider

If Dustin is the divider, he would aim to split the candies so that each half has a value of approximately $4 from his perspective.

One possible way to do this could involve allocating close to half of each type of candy based on his value preferences, but balancing to reach a value of $4 per share. Here’s one possible division that might work:

1. **50 Snickers** (50% of Snickers) valued at $50 \times 0.01 = 0.50$ dollars.
2. **50 Milky Ways** (50% of Milky Ways) valued at $50 \times 0.05 = 2.50$ dollars.
3. **50 Reese’s** (50% of Reese’s) valued at $50 \times 0.02 = 1.00$ dollar.

This division gives:
\[
0.50 + 2.50 + 1.00 = 4.00 \text{ dollars.}
\]

Thus, each half would be valued at $4 by Dustin, which he would consider a fair share.

---

### Summary of Answers:
1. **Value of this half in Dustin’s eyes**: $2.45.
2. **Is this a fair share for Dustin?** No, he values it at $2.45, less than the fair $4.
3. **Possible fair division by Dustin**: 50 Snickers, 50 Milky Ways, 50 Reese’s, totaling $4 per half.

---

Do you want more details on any part of this solution? Here are some related questions that could expand your understanding:

1. How would Kendra’s valuation affect what is considered a fair share?
2. Could Dustin create other fair divisions besides the one mentioned?
3. Why is the divider-chooser method commonly used for fair division?
4. How does changing Dustin's valuation of candies affect the division outcome?
5. If a third person joined the division, how would this change the process?

**Tip:** When dividing assets with different perceived values, try assigning values to each item to simplify determining a "fair" share.

Dustin and Kendra want to split a bag of fun-sized candy using the divider-chooser method. The bag contains 100 Snickers, 100 Milky Ways, and 100 Reese's, which Dustin values at $1, $5, and $2 respectively. If Kendra is the divider and puts 25 Snickers, 20 Milky Ways, and 60 Reese's in one half, answer the following: a. What is the value of this half in Dustin’s eyes? b. Does Dustin consider this a fair share? c. If Dustin was the divider, find a possible division that is consistent with his value system.

Explore a fair division problem involving candy, using the divider-chooser method. Dustin values Snickers, Milky Ways, and Reese’s differently, and we calculate the fairness of a division made by Kendra. Learn how to assess share value and create a balanced division based on individual valuation. Ideal for Grades 8-10.

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