To estimate the number of marbles in the bag, we will follow these steps:
1. Calculate the Mass of Only the Marbles in the Bag:
- The total mass of the marbles and the bag combined is 1123 grams.
- The mass of the bag alone is 68 grams.
- Therefore, the mass of the marbles alone is the total mass minus the mass of the bag.
[tex]\[
\text{Mass of marbles} = 1123 \, \text{grams} - 68 \, \text{grams} = 1055 \, \text{grams}
\][/tex]
2. Calculate the Mass of One Marble:
- The mass of 50 marbles is 250 grams.
- Therefore, the mass of one marble is:
[tex]\[
\text{Mass of one marble} = \frac{250 \, \text{grams}}{50} = 5 \, \text{grams}
\][/tex]
3. Determine the Number of Marbles in the Bag:
- To find how many marbles are in the bag, we divide the total mass of the marbles by the mass of one marble.
[tex]\[
\text{Number of marbles} = \frac{1055 \, \text{grams}}{5 \, \text{grams/marble}} = 211
\][/tex]
4. Round to Significant Figures:
- Here, the measurements provided (68 grams, 250 grams, 50 marbles, and 1123 grams) don't suggest the need for significant figure adjustments beyond basic rounding. The number of significant figures in the provided data, especially in the mass of 50 marbles and the bag's total mass, suggests that a standard answer without excessive precision is sufficient.
- Therefore, we simply report the answer as 211.
Thus, there are approximately 211 marbles in the bag.
