The band is breaking up and Rob, Sue, Tim and Vito each want the tour bus. Using the method of sealed bids, Rob bids $4200, Sue bids $4200, Tim bids $5900, and Vito bids $7700 for the bus. Since Vito's bid is the highest, he gets the bus and has to compensate the others to make the division fair. How much money will Rob get from Vito?

To determine how much money Rob will get from Vito using the sealed bids method, we need to follow these steps:

1. **Find the total of all the bids:**
   \[
   \text{Total of bids} = 4200 + 4200 + 5900 + 7700 = 22,000
   \]

2. **Find the fair share for each person:**
   Since there are 4 people, the fair share for each person is:
   \[
   \text{Fair share} = \frac{22,000}{4} = 5500
   \]
   Each person should get the value of $5500 in a fair division.

3. **Determine how much Vito needs to compensate:**
   Vito won the bus with his bid of $7700, which is greater than his fair share of $5500. Therefore, Vito needs to pay the difference between his bid and his fair share:
   \[
   \text{Amount Vito needs to pay} = 7700 - 5500 = 2200
   \]
   This $2200 will be distributed to the other participants.

4. **Distribute the compensation:**
   The $2200 will be distributed proportionally based on each person's fair share minus their bids. First, calculate the difference for Rob:
   \[
   \text{Rob's difference} = 5500 - 4200 = 1300
   \]

Since the total of differences for Rob, Sue, and Tim is:
   \[
   (1300 + 1300 + 600) = 3200
   \]

The compensation for Rob is proportional to his difference:
   \[
   \text{Rob's share of the compensation} = \frac{1300}{3200} \times 2200 = 893.75
   \]

Thus, Rob will get **$893.75** from Vito.

Would you like more details or have any questions?

Here are 5 related questions:
1. How much will Sue receive in compensation?
2. How much will Tim receive in compensation?
3. What if the bids were different, would Vito still get the bus?
4. How would the outcome change if the group size increased?
5. What if there was a tie for the highest bid?

**Tip:** In sealed bids, the winner compensates others based on the difference between their fair share and the highest bid.

Learn how to solve a fair division problem using the sealed bids method. Rob, Sue, Tim, and Vito each bid for a tour bus, and Vito wins with the highest bid. We break down how to fairly compensate the other participants, with a detailed calculation of Rob's share. Suitable for high school students, Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation