Let's solve the problem using the Sealed Bids Method for dividing assets between Tina and John.

Step 1: Record the Values

Each person's bid for the items is given in the table below.

• Tina's total bid for all the items: $10,200
• John's total bid for all the items: $9,400

Step 2: Determine Each Person's Fair Share

To calculate the fair share, divide each person’s total bid by the number of people (2).

• Tina's fair share: $\frac{10,200}{2} = 5,100$
• John's fair share: $\frac{9,400}{2} = 4,700$

Step 3: Allocate the Items

Allocate each item to the person who values it the most.

• Computer: John values it at $2,800, which is higher than Tina’s $2,500. Therefore, John gets the computer.
• Fridge: Tina values it at $4,000, which is higher than John’s $3,900. Therefore, Tina gets the fridge.
• Couch: Tina values it at $1,800, which is higher than John’s $1,600. Therefore, Tina gets the couch.
• TV: Tina values it at $1,900, which is higher than John’s $1,100. Therefore, Tina gets the TV.

Step 4: Calculate the Total Value of Items Each Person Receives

Next, calculate the value of the items each person gets according to their own bids.

• Tina's items: Fridge ($4,000) + Couch ($1,800) + TV ($1,900) = $7,700.
• John's items: Computer ($2,800).

Step 5: Cash Adjustment

The cash adjustment ensures that each person receives an amount equal to their fair share.

• Tina's total value is $7,700. Since her fair share is $5,100, she owes the difference: $7,700 - 5,100 = 2,600$ Therefore, Tina must pay $2,600 into the pool.

• John's total value is $2,800. Since his fair share is $4,700, he is short by: $4,700 - 2,800 = 1,900$ Therefore, John must receive $1,900 from the pool.

Step 6: Distribute the Cash

Tina's payment of $2,600 goes into the pool. John needs to receive $1,900 from the pool. The remaining balance in the pool is: $2,600 - 1,900 = 700$ The remaining $700 will go back to Tina.

Final Distribution:

• Tina receives: The fridge, couch, TV, and $700 in cash.
• John receives: The computer and $1,900 in cash.

This method ensures that each person receives their fair share based on their own valuations. Would you like further clarification on any part?

Additional Questions:

1. What happens if both Tina and John value an item equally?
2. How would the distribution change if a third person were added to the process?
3. How can this method be applied in dividing different types of assets (e.g., real estate)?
4. What are the advantages and disadvantages of the Sealed Bids Method?
5. How can the process be modified if one person prefers cash over items?

Tip: The Sealed Bids Method ensures that each party gets their fair share of the total value, with cash adjustments to account for differences in item allocation.