The problem states that the packing box is designed to hold 25 kg, with a tolerance of plus or minus 0.8 kg.

To find the greatest weight the box can hold, we add the tolerance to the designed weight:

$\text{Greatest weight} = 25 \, \text{kg} + 0.8 \, \text{kg} = 25.8 \, \text{kg}$

Thus, the greatest weight the box can hold is 25.8 kg.

Would you like more details or have any other questions?

Here are 5 related questions to explore:

1. What is the least weight the box can hold, given the same tolerance?
2. How would the result change if the tolerance was 1 kg instead of 0.8 kg?
3. If the designed weight increased to 30 kg with the same tolerance, what would be the greatest weight?
4. What would the average weight range be, given the tolerance of 0.8 kg?
5. How does tolerance affect the overall capacity of containers in real-life scenarios?

Tip: When dealing with tolerances in weight or measurements, always apply both the positive and negative ranges to fully understand the capacity or limits.