Alright, let's tackle this step-by-step:
1. Determine the total mass of the markers only:
We start by subtracting the mass of the box from the total mass of the markers and the box:
[tex]\[
\text{Total mass of markers} = 658 \text{ grams (mass of markers + box)} - 76 \text{ grams (mass of box only)}
\][/tex]
[tex]\[
\text{Total mass of markers} = 582 \text{ grams}
\][/tex]
2. Understand the mass of a specific number of markers:
We know that 10 markers have a total mass of 142 grams. To find the mass of a single marker:
[tex]\[
\text{Mass of one marker} = \frac{142 \text{ grams}}{10} = 14.2 \text{ grams}
\][/tex]
3. Calculate the approximate number of markers in the box:
To find the number of markers, we need to divide the total mass of markers by the mass of a single marker:
[tex]\[
\text{Number of markers} = \frac{582 \text{ grams (total mass of markers)}}{142 \text{ grams (mass of 10 markers)} \div 10}
\][/tex]
Simplifying:
[tex]\[
\text{Number of markers} = \frac{582 \text{ grams}}{14.2 \text{ grams}}
\][/tex]
4. Perform the division:
This division yields:
[tex]\[
\frac{582}{14.2} \approx 41
\][/tex]
5. Adjust for significant figures:
Given the precision requirement, we round to significant figures:
[tex]\[
\text{Number of markers} \approx 4.1
\][/tex]
Therefore, the estimated number of markers in the box, using significant figures, is approximately:
[tex]\(\boxed{4.1}\)[/tex]
