Answer :
To determine how many boxes Crystal needs to hold all her compact discs, let's work through the problem step by step:
1. Understand the Problem:
- Crystal has a total of 94 compact discs.
- Each box can hold up to 16 discs.
2. Determine How Many Boxes Are Needed:
- We need to find out how many boxes are required to hold all 94 discs. To do this, we perform a division of the total number of discs by the number of discs each box can hold.
- Divide 94 by 16 to determine the number of full boxes needed.
- [tex]\(\frac{94}{16} = 5.875\)[/tex]. This means Crystal would need a little under 6 full boxes.
3. Round Up:
- Since it’s not possible to use a fraction of a box, we must round up. Rounding 5.875 up gives us 6.
- Thus, Crystal will need 6 boxes to ensure all 94 discs are stored.
4. Select the Correct Mathematical Sentence:
- Now, let's see which option best matches.
- The problem is about how many boxes are sufficient for 94 discs, and the expression must show enough boxes. Thus, we’re looking for an inequality that ensures at least 94 discs are contained.
- Option D, [tex]\(16b \geq 94\)[/tex], accurately represents this situation. It shows that the total capacity of the boxes (16 discs per box times the number of boxes) must be at least 94 discs.
Therefore, the mathematical sentence that most accurately expresses the information in the problem is Option D: [tex]\(16b \geq 94\)[/tex]. Crystal needs 6 boxes to store all her discs.
1. Understand the Problem:
- Crystal has a total of 94 compact discs.
- Each box can hold up to 16 discs.
2. Determine How Many Boxes Are Needed:
- We need to find out how many boxes are required to hold all 94 discs. To do this, we perform a division of the total number of discs by the number of discs each box can hold.
- Divide 94 by 16 to determine the number of full boxes needed.
- [tex]\(\frac{94}{16} = 5.875\)[/tex]. This means Crystal would need a little under 6 full boxes.
3. Round Up:
- Since it’s not possible to use a fraction of a box, we must round up. Rounding 5.875 up gives us 6.
- Thus, Crystal will need 6 boxes to ensure all 94 discs are stored.
4. Select the Correct Mathematical Sentence:
- Now, let's see which option best matches.
- The problem is about how many boxes are sufficient for 94 discs, and the expression must show enough boxes. Thus, we’re looking for an inequality that ensures at least 94 discs are contained.
- Option D, [tex]\(16b \geq 94\)[/tex], accurately represents this situation. It shows that the total capacity of the boxes (16 discs per box times the number of boxes) must be at least 94 discs.
Therefore, the mathematical sentence that most accurately expresses the information in the problem is Option D: [tex]\(16b \geq 94\)[/tex]. Crystal needs 6 boxes to store all her discs.
