Four heirs (A, B, C, and D) must fairly divide an estate consisting of two items - a house and a car - using the method of sealed bids. The players' bids (in dollars) are:



ABCDHouse

232000

224000

231000

230000

Car

32000

28000

29000

30000


The original fair share of A is worth: $ 

In the initial allocation, player A:
Select an answer and  pays to gets from Correct the estate $

After all is said and done, in the final allocation, player A:
Select an answer Gets the house Gets the car Gets no items Gets the house and car Correct and Select an answer gets from pays to Correct the estate $

### Step 1: Determine the total value of the estate
The total estate consists of the house and the car. The total value of each item is determined by averaging the bids from the four heirs.

**Total value of the house:**
\[
\frac{232000 + 224000 + 231000 + 230000}{4} = \frac{917000}{4} = 229250
\]

**Total value of the car:**
\[
\frac{32000 + 28000 + 29000 + 30000}{4} = \frac{119000}{4} = 29750
\]

**Total estate value:**
\[
229250 + 29750 = 259000
\]

### Step 2: Determine the fair share of each heir
Each heir’s fair share is one-fourth of the total estate value.

\[
\frac{259000}{4} = 64750
\]

Thus, the fair share of **A** is **$64,750**.

### Step 3: Initial allocation
The items are allocated to the highest bidder for each item:

- **House:** A bids $232,000, the highest bid, so A receives the house.
- **Car:** A bids $32,000, the highest bid, so A receives the car.

Thus, in the **initial allocation**, player A gets both the house and the car.

### Step 4: Payments to or from the estate
- A has received items worth $232,000 (house) + $32,000 (car) = **$264,000**.
- A’s fair share is $64,750.

Thus, A owes to the estate:
\[
264000 - 64750 = 199250
\]

### Step 5: Final allocation
After all is done, in the **final allocation**, player A:
- **Gets the house and the car**.
- **Pays $199,250** to the estate.

### Summary:

1. **Original fair share of A:** $64,750
2. **Initial allocation:** Player A gets the house and the car, and owes $199,250 to the estate.
3. **Final allocation:** Player A gets the house and the car, and pays $199,250 to the estate.

Would you like further details on any of the steps?

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Here are 5 relative questions to expand your understanding:

1. How would the calculation change if there were three heirs instead of four?
2. What happens if the bids for the house and car tie?
3. How would A’s payment change if A didn’t get the car but still got the house?
4. How is the surplus distributed if the total payments to the estate exceed the fair shares?
5. Can the same method be applied if there are more than two items in the estate?

**Tip:** When using sealed bids, always ensure each player values their fair share based on the average value of the items in the estate, not just their own bids.

Four heirs (A, B, C, and D) must fairly divide an estate consisting of two items - a house and a car - using the method of sealed bids. The players' bids (in dollars) are: House: A: 232000, B: 224000, C: 231000, D: 230000 Car: A: 32000, B: 28000, C: 29000, D: 30000. The original fair share of A is worth: $ In the initial allocation, player A: Select an answer and pays to gets from the estate $ After all is said and done, in the final allocation, player A: Select an answer Gets the house Gets the car Gets no items Gets the house and car and pays to gets from the estate $

Learn how to fairly divide an estate using sealed bids in this example involving four heirs and two items: a house and a car. The solution covers key concepts such as averages, fair share calculation, and determining payments owed to or from the estate. Suitable for students in Grades 9-12.

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