For all your questions, big or small, IDNLearn.com has the answers you need. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.

Given the following data, estimate the number of markers in the box. Round your answer to the nearest whole number using significant figures.

- Total Mass (Markers + Box): 658 grams
- Mass of 10 Markers: 142 grams
- Mass of Box Only: 76 grams

How many markers are in the box?


Sagot :

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]