The problem states that Severin works in a factory where the bolts have a nominal mass of 5 grams each, but each bolt's mass can vary by up to ±1.9%. The total mass of the bolts in the box is exactly 1 kg (1000 grams). We are asked to determine the minimum and maximum number of bolts that could be in the box.

Step 1: Calculate the mass range for a single bolt

The mass of each bolt can vary by 1.9%. The nominal mass is 5 grams, so:

• Maximum mass of one bolt: $5 \, \text{g} + 1.9\% \times 5 \, \text{g} = 5 + 0.095 = 5.095 \, \text{g}$

• Minimum mass of one bolt: $5 \, \text{g} - 1.9\% \times 5 \, \text{g} = 5 - 0.095 = 4.905 \, \text{g}$

Step 2: Determine the number of bolts in the box

We know the total mass of the bolts is 1000 grams.

• Maximum number of bolts: The maximum number of bolts would occur if each bolt had the minimum possible mass, $4.905 \, \text{g}$. The number of bolts, $n$, would be: $n = \frac{1000 \, \text{g}}{4.905 \, \text{g}} \approx 203.86$ Since $n$ must be a whole number, we round this down to $203$ bolts.

• Minimum number of bolts: The minimum number of bolts would occur if each bolt had the maximum possible mass, $5.095 \, \text{g}$. The number of bolts would be: $n = \frac{1000 \, \text{g}}{5.095 \, \text{g}} \approx 196.24$ We round this down to $196$ bolts.

Final Answer:

• Minimum number of bolts: 196
• Maximum number of bolts: 203

Would you like further clarification or details on this problem?

Here are 5 related questions to expand your understanding:

1. How would the solution change if the variation in mass was ±2% instead of ±1.9%?
2. What would happen if the total mass of the bolts was not exactly 1 kg but 2 kg?
3. Can you calculate the total mass for a specific number of bolts with average mass variations?
4. How would the problem change if the percentage variation was not symmetric (i.e., +1.9% but −1.5%)?
5. How could you solve this if the bolts were packed in groups, and each group's mass varied?

Tip: When calculating variations, always consider the range and ensure your results are properly rounded to reflect real-world scenarios (e.g., whole number of objects like bolts).