As part of an inheritance, three children, Abby, Ben and Carla, are dividing four vehicles using Sealed Bids. Their bids (in thousands of dollars) for each item is shown below.

 	Abby	Ben	Carla
Motorcycle	11	10	7
Car	8	14	13
Tractor	6	3	4
Boat	6	3	5
In the final allocation, Abby gets which items?  (click none, one, or multiple boxes)

Motorcycle
Car
Tractor
Boat
In addition, she 
Select an answer
 to/from the estate: $

Give your answer to the last question to the nearest dollar (careful here - the original amounts were in thousands of dollars)

The **Sealed Bids** method for dividing items in inheritance works by having each participant bid on the items. The estate is then divided based on the value each participant places on the items, and an equal share of the total value is calculated for each participant. The difference between what each person receives and their fair share is compensated by paying to or receiving from the estate.

### Step-by-Step Solution:

1. **Total Bids for Each Item**:
   - Motorcycle: Abby (11) + Ben (10) + Carla (7) = 28 thousand dollars
   - Car: Abby (8) + Ben (14) + Carla (13) = 35 thousand dollars
   - Tractor: Abby (6) + Ben (3) + Carla (4) = 13 thousand dollars
   - Boat: Abby (6) + Ben (3) + Carla (5) = 14 thousand dollars

2. **Fair Share Calculation**:
   - Total sum of bids = 28 + 35 + 13 + 14 = 90 thousand dollars
   - Each person’s fair share = Total bids / 3 = 90 / 3 = 30 thousand dollars

3. **Item Allocation**:
   The person who bids the highest on an item receives that item.
   - **Motorcycle**: Abby (11) vs Ben (10) vs Carla (7) → Abby wins the motorcycle.
   - **Car**: Ben (14) vs Abby (8) vs Carla (13) → Ben wins the car.
   - **Tractor**: Abby (6) vs Carla (4) vs Ben (3) → Abby wins the tractor.
   - **Boat**: Carla (5) vs Abby (6) vs Ben (3) → Abby wins the boat.

   So, **Abby gets the motorcycle, the tractor, and the boat**.

4. **Value of Items Abby Receives**:
   - Motorcycle: 11 thousand dollars
   - Tractor: 6 thousand dollars
   - Boat: 6 thousand dollars
   - Total value of Abby’s items = 11 + 6 + 6 = 23 thousand dollars

5. **Adjustment**:
   Abby's fair share is 30 thousand dollars, but she only received 23 thousand dollars in items. Therefore, Abby is **entitled to receive money from the estate**.
   
   The amount Abby will receive = Fair share - Value of items received
   = 30,000 - 23,000
   = 7,000 dollars.

### Final Answer:
- Abby receives the **Motorcycle, Tractor, and Boat**.
- She is entitled to receive **$7,000 from the estate**.

Would you like any more details or have any further questions?

Here are 5 related questions:
1. How is the estate total calculated if there were 5 items instead of 4?
2. What happens if multiple people bid the same amount on an item?
3. How would the allocation change if the bids were much closer together?
4. How does the Sealed Bids method ensure fairness?
5. What happens if a participant bids more than their fair share?

**Tip**: Always calculate the fair share by dividing the total estate value by the number of participants before determining who owes or receives money.

As part of an inheritance, three children, Abby, Ben and Carla, are dividing four vehicles using Sealed Bids. Their bids (in thousands of dollars) for each item is shown below.

  Abby   Ben   Carla
Motorcycle  11   10   7
Car   8   14   13
Tractor   6   3   4
Boat   6   3   5
In the final allocation, Abby gets which items? (click none, one, or multiple boxes)
Motorcycle
Car
Tractor
Boat
In addition, she receives an amount to/from the estate: $
Give your answer to the last question to the nearest dollar (careful here - the original amounts were in thousands of dollars).

Discover how Abby, Ben, and Carla use the Sealed Bids method to fairly divide four vehicles. This problem covers the fair share calculation, item allocation, and the final adjustment for Abby. Learn key concepts in asset division and proportionality.

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