Certainly! Let's solve this step by step.
1. Identify the given data:
- Total mass of the jar and paper clips combined = 713 grams
- Mass of 50 paper clips = 51 grams
- Mass of the jar alone = 89 grams
2. Calculate the mass of the paper clips alone:
To find the mass of just the paper clips, we need to subtract the mass of the jar from the total mass.
[tex]\[
\text{Mass of paper clips} = \text{Total mass} - \text{Mass of jar} = 713 \text{ grams} - 89 \text{ grams} = 624 \text{ grams}
\][/tex]
3. Calculate the mass of one paper clip:
Given that 50 paper clips weigh 51 grams, the mass of one paper clip can be found by dividing the total mass of the 50 paper clips by the number of paper clips.
[tex]\[
\text{Mass of one paper clip} = \frac{\text{Mass of 50 paper clips}}{50} = \frac{51 \text{ grams}}{50} = 1.02 \text{ grams}
\][/tex]
4. Estimate the number of paper clips in the jar:
Using the mass of the paper clips alone and the mass of one paper clip, we can estimate the total number of paper clips in the jar by dividing the mass of the paper clips by the mass of one paper clip.
[tex]\[
\text{Number of paper clips} = \frac{\text{Mass of paper clips}}{\text{Mass of one paper clip}} = \frac{624 \text{ grams}}{1.02 \text{ grams}} = 611.7647058823529
\][/tex]
5. Round the answer to the nearest whole number using significant figures:
Since we are dealing with practical items (paper clips), it is reasonable to round our answer to the nearest whole number.
[tex]\[
\text{Number of paper clips} \approx 612
\][/tex]
Therefore, the estimated number of paper clips in the jar is approximately 612.
