Certainly! Let's break down the solution step-by-step.
1. Given Data
- Total mass (crayons + box): [tex]\(536\)[/tex] grams
- Mass of [tex]\(8\)[/tex] crayons: [tex]\(45\)[/tex] grams
- Mass of the box: [tex]\(63\)[/tex] grams
2. Find the mass of just the crayons
To determine the mass of only the crayons, we need to subtract the mass of the box from the total mass:
[tex]\[
\text{Mass of crayons} = \text{Total mass} - \text{Mass of the box}
\][/tex]
Substituting the given values,
[tex]\[
\text{Mass of crayons} = 536 \text{ grams} - 63 \text{ grams} = 473 \text{ grams}
\][/tex]
3. Determine the mass of a single crayon
We know the mass of [tex]\(8\)[/tex] crayons is [tex]\(45\)[/tex] grams. Therefore, the mass of a single crayon is:
[tex]\[
\text{Mass of one crayon} = \frac{45 \text{ grams}}{8} = 5.625 \text{ grams}
\][/tex]
4. Calculate the number of crayons in the box
To find the number of crayons, we divide the total mass of the crayons by the mass of a single crayon:
[tex]\[
\text{Number of crayons} = \frac{\text{Mass of crayons}}{\text{Mass of one crayon}} = \frac{473 \text{ grams}}{5.625 \text{ grams}} \approx 84.08888888888889
\][/tex]
5. Round the answer by using significant figures
Given the initial data and typical rounding practices, we should round to one significant figure:
[tex]\[
\text{Rounded number of crayons} \approx 80
\][/tex]
So, the estimated number of crayons in the box is approximately [tex]\(80\)[/tex].
