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The problem in the image is:

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In a tug-of-war team of 10 members, the average weight of all participants is 66 kg. If the five heaviest individuals, whose weights are in ascending order \( A < B < C < D < E \), are excluded, the average weight of the remaining members drops by 3 kg. What is the maximum possible weight (in integral multiple of kgs) of \( A \)?

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### Step-by-step breakdown:

1. **Total weight of the team**:
   - There are 10 members, and the average weight of all participants is 66 kg.
   - Total weight = \( 10 \times 66 = 660 \, \text{kg} \).

2. **Excluding the heaviest 5 members**:
   - After excluding the heaviest 5 members, the average weight of the remaining 5 members drops by 3 kg. The new average becomes \( 66 - 3 = 63 \, \text{kg} \).
   - The total weight of the lighter 5 members = \( 5 \times 63 = 315 \, \text{kg} \).

3. **Weight of the heaviest 5 members**:
   - The total weight of all members is 660 kg, and the total weight of the lighter 5 members is 315 kg.
   - Therefore, the total weight of the heaviest 5 members is \( 660 - 315 = 345 \, \text{kg} \).

4. **Maximizing \( A \)'s weight**:
   - The weights of the 5 heaviest members are \( A < B < C < D < E \), and their total weight is 345 kg.
   - To maximize \( A \), the weights of \( B, C, D, \) and \( E \) should be as large as possible while still satisfying the total weight of 345 kg.
   - Assume \( A = x \), and \( B, C, D, E \) must sum up to \( 345 - x \). To maximize \( x \), we want to make \( B, C, D, \) and \( E \) as large as possible.

Since the weights of the heaviest 5 members must be in increasing order, we need to calculate the maximum value of \( A \) given the other constraints.The maximum possible weight of \( A \) (the lightest of the 5 heaviest members) is 67 kg.

Would you like a detailed breakdown or further explanation of any part of the solution? Here are 5 related questions to expand your understanding:

1. How do averages change when certain members are removed from a group?
2. What is the effect of evenly distributing weights on maximizing or minimizing a value?
3. How does the order of weights (ascending vs. descending) affect optimization problems?
4. Can the sum of consecutive numbers help in solving problems involving increasing order?
5. How does solving equations involving constraints relate to real-world scenarios?

**Tip**: When maximizing or minimizing variables in problems with constraints, always try to set the remaining variables as large or small as possible while respecting the given conditions.

In a tug-of-war team of 10 members, the average weight of all participants is 66 kg. If the five heaviest individuals, whose weights are in ascending order A < B < C < D < E, are excluded, the average weight of the remaining members drops by 3 kg. What is the maximum possible weight (in integral multiple of kgs) of A?

Solve a tug-of-war problem involving averages, maximization, and inequalities. Learn how to calculate the maximum possible weight of a participant, with a step-by-step breakdown. Suitable for high school students.

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