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.
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