Answer :
Sure, let's break down the problem and find the correct mathematical sentence that expresses the situation described.
### Problem Analysis:
- Crystal has 94 compact discs.
- Each box can hold 16 discs.
- We need to determine how many boxes Crystal will need to hold all 94 discs.
### Solution Approach:
1. Calculate the Number of Boxes:
To find out how many boxes Crystal needs, we divide the total number of discs by the capacity of one box.
[tex]\[
\text{Number of boxes} = \frac{94 \text{ discs}}{16 \text{ discs per box}}
\][/tex]
2. Handling Remainders:
Because we can't have a fraction of a box and every box needs to be completely filled, we round up to the next whole number if there’s a remainder. This ensures all discs are contained.
3. Interpretation:
If there’s a need to round up, it implies that the number of boxes times 16 discs per box should be at least 94 discs.
Following the above reasoning, we need to express the scenario where:
[tex]\[
16b \geq 94
\][/tex]
Here, [tex]\( b \)[/tex] represents the number of boxes Crystal needs.
### Conclusion:
Based on the information and analysis, the most accurate mathematical sentence that represents the problem is:
[tex]\[
\boxed{16b \geq 94}
\][/tex]
Option C: [tex]\( 16 b \geq 94 \)[/tex] is correct.
### Problem Analysis:
- Crystal has 94 compact discs.
- Each box can hold 16 discs.
- We need to determine how many boxes Crystal will need to hold all 94 discs.
### Solution Approach:
1. Calculate the Number of Boxes:
To find out how many boxes Crystal needs, we divide the total number of discs by the capacity of one box.
[tex]\[
\text{Number of boxes} = \frac{94 \text{ discs}}{16 \text{ discs per box}}
\][/tex]
2. Handling Remainders:
Because we can't have a fraction of a box and every box needs to be completely filled, we round up to the next whole number if there’s a remainder. This ensures all discs are contained.
3. Interpretation:
If there’s a need to round up, it implies that the number of boxes times 16 discs per box should be at least 94 discs.
Following the above reasoning, we need to express the scenario where:
[tex]\[
16b \geq 94
\][/tex]
Here, [tex]\( b \)[/tex] represents the number of boxes Crystal needs.
### Conclusion:
Based on the information and analysis, the most accurate mathematical sentence that represents the problem is:
[tex]\[
\boxed{16b \geq 94}
\][/tex]
Option C: [tex]\( 16 b \geq 94 \)[/tex] is correct.
