To determine which items Abby gets and the amount she owes or receives from the estate, we can follow the Sealed Bid procedure. In this procedure:

1. Each participant bids on the items.
2. The highest bid for each item wins, and the person who bid the highest gets the item.
3. Once the items are allocated, the total amount paid by each person (their bid) is compared to the total amount each person "should" have paid, based on the total value of the items they received.

Step 1: Determine who wins each item

• Motorcycle: Abby bid 12, Ben bid 10, Carla bid 7. Abby wins the motorcycle.
• Car: Abby bid 10, Ben bid 12, Carla bid 9. Ben wins the car.
• Tractor: Abby bid 3, Ben bid 5, Carla bid 4. Ben wins the tractor.
• Boat: Abby bid 7, Ben bid 6, Carla bid 4. Abby wins the boat.

Step 2: Calculate total value of items for each person

• Abby gets the Motorcycle (12), and the Boat (7), so her total "value" is $12 + 7 = 19$.
• Ben gets the Car (12) and the Tractor (5), so his total "value" is $12 + 5 = 17$.
• Carla gets no items, so her total value is 0.

Step 3: Determine what Abby owes or receives

The total value of all items is $12 + 12 + 5 + 7 = 36$.

If the total value of the items is 36, each child should pay $\frac{36}{3} = 12$.

• Abby has won items worth 19, but she should only pay 12. Therefore, Abby is entitled to 7 (since she overpaid).
• Ben has won items worth 17, but he should pay 12, so he owes 5 to the estate.
• Carla has won no items, so she owes the full amount of 12.

Final Allocation:

• Abby gets: Motorcycle, Boat.
• Abby is entitled to: 7 from the estate (she overpaid).

Summary:

• Abby gets: Motorcycle, Boat
• Abby is entitled to: $7,000 (7 thousand dollars)

If you need more clarification or have questions about this process, feel free to ask! Here are some follow-up questions you might find interesting:

1. How are Sealed Bid auctions used in real-life situations besides inheritance?
2. What happens if two people bid the same amount on the same item?
3. Can you modify the bidding process to allow for ties?
4. How do you adjust the bidding process if some participants are unwilling or unable to pay their bids?
5. What role does fairness play in a bidding process like this one?

Tip: Always double-check each participant's bid and the total amounts to ensure you’re correctly distributing the items.