Severin works in a factory that produces steel bolts. one type of steel bolt should have the mass of 5g; however, there is some variation, so each bolt may be heavier or lighter by as much as 1.9%. Severin puts together a box of these bolts and notices that the total mass of the box is exactly 1kg. Determine the minimum and maximum number of bolts that could be in the box.

The mass of each steel bolt is approximately 5g, but there is a variation of ±1.9%. This means that each bolt can have a mass between:

\[
5g \times (1 - 0.019) = 5g \times 0.981 = 4.905g
\]
(minimum mass) and
\[
5g \times (1 + 0.019) = 5g \times 1.019 = 5.095g
\]
(maximum mass).

The total mass of the box is 1kg, or 1000g.

### Step 1: Maximum number of bolts
To get the maximum number of bolts, we assume each bolt has the minimum mass of 4.905g:
\[
\text{Number of bolts} = \frac{1000g}{4.905g/bolt} \approx 203.86
\]
Since we can't have a fraction of a bolt, we round down to 203 bolts.

### Step 2: Minimum number of bolts
To get the minimum number of bolts, we assume each bolt has the maximum mass of 5.095g:
\[
\text{Number of bolts} = \frac{1000g}{5.095g/bolt} \approx 196.26
\]
We round down to 196 bolts.

### Conclusion
- The **maximum** number of bolts is **203**.
- The **minimum** number of bolts is **196**.

Would you like a more detailed explanation or clarification?

Here are some related questions:
1. How do you calculate the percentage variation for different mass values?
2. What impact does rounding have in real-world measurements like this?
3. How could Severin measure the exact number of bolts in the box?
4. What are other methods to estimate the mass of individual bolts if only total mass is known?
5. How would changing the percentage variation affect the possible number of bolts?

**Tip:** Always ensure you understand the range of error or variation when dealing with measurements to avoid underestimating or overestimating values.

Severin works in a factory that produces steel bolts. One type of steel bolt should have the mass of 5g; however, there is some variation, so each bolt may be heavier or lighter by as much as 1.9%. Severin puts together a box of these bolts and notices that the total mass of the box is exactly 1kg. Determine the minimum and maximum number of bolts that could be in the box.

Learn how to determine the minimum and maximum number of steel bolts in a 1kg box, with each bolt having a mass of 5g ± 1.9%. This solution involves percentage variation and mass calculation, suitable for students in Grades 9-12.

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