- Determine the mass of the jellybeans alone: \(198 - 32 = 166 \text{ g}\).
- Find the average mass per jellybean: \(23 / 15 \approx 1.533 \text{ g}\).
- Calculate the total count: \(166 \div (23/15) \approx 108.26\).
- Round to the nearest whole number: \(\boxed{108}\).
Explanation
- Calculate the mass of the jellybeans
To estimate the number of jellybeans in the bag, we first determine the mass of the jellybeans themselves by subtracting the mass of the empty bag from the total mass. The total mass of the bag with the jellybeans is \(198 \text{ grams}\), and the mass of the bag alone is \(32 \text{ grams}\). Thus, the mass of the jellybeans is:
\[198 \text{ grams} - 32 \text{ grams} = 166 \text{ grams}.\]
- Calculate the mass of a single jellybean
Next, we determine the average mass of a single jellybean. We are given that \(15\) jellybeans have a mass of \(23 \text{ grams}\). Therefore, the mass of one jellybean is:
\[\frac{23 \text{ grams}}{15} \approx 1.5333 \text{ grams per jellybean}.\]
- Determine the number of jellybeans
To find the total number of jellybeans in the bag, we divide the total mass of the jellybeans by the mass of a single jellybean:
\[\text{Number of jellybeans} = \frac{166}{23 / 15} = 166 \times \frac{15}{23} = \frac{2490}{23} \approx 108.26.\]
Since the number of jellybeans must be a whole number, we round \(108.26\) to the nearest whole number, which is \(108\).
Examples
Estimation is a valuable skill in everyday life and science. Just as we estimated the number of jellybeans here, you can use this method to estimate quantities in other scenarios, such as determining the number of items in a large container by weighing a small sample or calculating the number of pages in a book based on the thickness of a few pages. This approach saves time when counting large quantities individually is impractical.