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:

A	B	C	D
House	236000	229000	235000	225000
Car	32000	28000	33000	29000


The original fair share of A is worth: $ 


In the initial allocation, player A:

Select an answer
 and 
Select an answer
 the estate $


After all is said and done, in the final allocation, player A:

Select an answer
 and 
Select an answer
 the estate $


To solve this problem, we will use the method of sealed bids to fairly divide the estate between the four heirs (A, B, C, and D). Here's the process:

### Step 1: Calculate the Total Value and Fair Share
1. **Total Value of Each Player's Bid**: 
   - For each player, the total value of their bid is the sum of their bid for the house and the car.
   - Fair Share for each player is their total bid divided by the number of players (4).

\[
\text{Total Bid of Player } A = 236,000 + 32,000 = 268,000
\]
\[
\text{Total Bid of Player } B = 229,000 + 28,000 = 257,000
\]
\[
\text{Total Bid of Player } C = 235,000 + 33,000 = 268,000
\]
\[
\text{Total Bid of Player } D = 225,000 + 29,000 = 254,000
\]

2. **Calculate the Fair Share for Each Player**:

\[
\text{Fair Share of Player } A = \frac{268,000}{4} = 67,000
\]
\[
\text{Fair Share of Player } B = \frac{257,000}{4} = 64,250
\]
\[
\text{Fair Share of Player } C = \frac{268,000}{4} = 67,000
\]
\[
\text{Fair Share of Player } D = \frac{254,000}{4} = 63,500
\]

Thus, the fair share of player A is **$67,000**.

### Step 2: Determine the Initial Allocation
To determine who gets which item, we allocate each item to the player who bid the highest for it:

- **House**:  
  - A: 236,000  
  - B: 229,000  
  - C: 235,000  
  - D: 225,000  

  The highest bid for the house is **A** with **$236,000**.

- **Car**:  
  - A: 32,000  
  - B: 28,000  
  - C: 33,000  
  - D: 29,000  

  The highest bid for the car is **C** with **$33,000**.

### Initial Allocation:
- **Player A** gets the **House**.
- **Player C** gets the **Car**.

### Step 3: Determine the Payment to the Estate
Now, we calculate the amount each player must pay to the estate:

- **Player A** receives the house valued at their bid of $236,000.
  - Their fair share is $67,000.
  - **Payment to Estate by A** = $236,000 - 67,000 = 169,000$.

- **Player C** receives the car valued at their bid of $33,000.
  - Their fair share is $67,000.
  - **Payment to Estate by C** = $33,000 - 67,000 = -34,000$.  
  - This means player C should **receive $34,000** from the estate.

The estate collects $169,000 from Player A and gives $34,000 to Player C, resulting in a net estate amount of $135,000.

### Final Allocation:
1. **Player A**: Receives the **House** and pays **$169,000** to the estate.
2. **Player C**: Receives the **Car** and receives **$34,000** from the estate.

### Conclusion:
- The original fair share of A is **$67,000**.
- In the initial allocation, player A **receives the house** and **pays $169,000** to the estate.
- In the final allocation, player A **receives the house** and **pays $169,000** to the estate.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How is the total surplus handled in this allocation method?
2. What happens if two players bid the same highest amount for an item?
3. Can this method be extended to more players or items?
4. How would this method change if the estate had liabilities?
5. What are some other methods for fair division besides sealed bids?

**Tip**: In fair division problems, understanding each player's valuation of items and how payments balance the allocation is key to ensuring fairness.

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: A: House 236,000, Car 32,000; B: House 229,000, Car 28,000; C: House 235,000, Car 33,000; D: House 225,000, Car 29,000. The original fair share of A is worth: $ In the initial allocation, player A: Select an answer and Select an answer the estate $ After all is said and done, in the final allocation, player A: Select an answer and Select an answer the estate $

Explore how to fairly divide an estate using the sealed bids method in a situation with four heirs bidding on a house and a car. Learn how to calculate fair shares, allocate items, and determine payments to the estate. Ideal for students in Grades 10-12.

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