Calculating Average Weight of Remaining Boxes

The problem asks for the average weight of the remaining boxes after removing the heaviest and lightest ones from a set of 10 boxes.

Initial Data Analysis

• Total number of boxes: 10
• Average weight of 10 boxes: 15.5 kg
• Weight of the heaviest box: 21 kg
• Weight of the lightest box: 10 kg

Step 1: Calculate Total Weight

The total weight of all 10 boxes is found by multiplying the average weight by the number of boxes.

Total Weight = Average Weight × Number of Boxes

LaTeX representation:
Total Weight = $15.5 \text{ kg} \times 10 = 155 \text{ kg}$

Step 2: Calculate Weight of Removed Boxes

The weights of the heaviest and lightest boxes are given. Their combined weight is:

Weight of Removed Boxes = Weight of Heaviest Box + Weight of Lightest Box

LaTeX representation:
Weight of Removed Boxes = $21 \text{ kg} + 10 \text{ kg} = 31 \text{ kg}$

Step 3: Calculate Remaining Weight

Subtract the weight of the removed boxes from the total weight to find the weight of the remaining boxes.

Remaining Weight = Total Weight - Weight of Removed Boxes

LaTeX representation:
Remaining Weight = $155 \text{ kg} - 31 \text{ kg} = 124 \text{ kg}$

Step 4: Calculate Number of Remaining Boxes

After removing the heaviest and lightest boxes, the number of remaining boxes is:

Number of Remaining Boxes = Total Boxes - 2

LaTeX representation:
Number of Remaining Boxes = $10 - 2 = 8$

Step 5: Calculate Average Weight of Remaining Boxes

Finally, divide the remaining weight by the number of remaining boxes to find the new average weight.

Average Weight of Remaining Boxes = Remaining Weight / Number of Remaining Boxes

LaTeX representation:
Average Weight of Remaining Boxes = $\frac{124 \text{ kg}}{8} = 15.5 \text{ kg}$

Conclusion

The average weight of the remaining 8 boxes is 15.5 kg.