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Answer :
To determine how many boxes Crystal will need for all of her compact discs, let's break down the steps:
1. Understand the Problem:
Crystal has 94 compact discs and each box can hold 16 discs. We need to find out how many boxes she will need to put all of the discs away.
2. Calculate the Minimum Number of Boxes:
- To find the number of boxes needed, we divide the total number of discs by the number of discs each box can hold:
[tex]\[
\text{Total discs} = 94, \quad \text{Discs per box} = 16
\][/tex]
[tex]\[
\text{Number of boxes needed} = \lceil \frac{94}{16} \rceil
\][/tex]
3. Interpret the Choices:
- Option A: [tex]\(b + 16 = 94\)[/tex] suggests adding 16 to a number to get 94, which doesn't relate to our division problem.
- Option B: [tex]\(94 - b = 16\)[/tex] suggests subtracting a number from 94 to get 16, which also doesn't fit.
- Option C: [tex]\(16b < 94\)[/tex] implies the total capacity of all boxes is less than 94, which wouldn't ensure all discs fit.
- Option D: [tex]\(16b \geq 94\)[/tex] states the total capacity of the boxes must be at least 94, ensuring all discs fit, which makes sense given the problem needs all discs stored.
Hence, the choice that matches the mathematical sentence needed to express how many boxes Crystal needs is:
Option D: [tex]\(16b \geq 94\)[/tex]
This inequality means we need enough boxes so that their total capacity (16 discs per box) meets or exceeds the total number of discs, 94. Using such boxes, Crystal will need 6 boxes to store all her discs.
1. Understand the Problem:
Crystal has 94 compact discs and each box can hold 16 discs. We need to find out how many boxes she will need to put all of the discs away.
2. Calculate the Minimum Number of Boxes:
- To find the number of boxes needed, we divide the total number of discs by the number of discs each box can hold:
[tex]\[
\text{Total discs} = 94, \quad \text{Discs per box} = 16
\][/tex]
[tex]\[
\text{Number of boxes needed} = \lceil \frac{94}{16} \rceil
\][/tex]
3. Interpret the Choices:
- Option A: [tex]\(b + 16 = 94\)[/tex] suggests adding 16 to a number to get 94, which doesn't relate to our division problem.
- Option B: [tex]\(94 - b = 16\)[/tex] suggests subtracting a number from 94 to get 16, which also doesn't fit.
- Option C: [tex]\(16b < 94\)[/tex] implies the total capacity of all boxes is less than 94, which wouldn't ensure all discs fit.
- Option D: [tex]\(16b \geq 94\)[/tex] states the total capacity of the boxes must be at least 94, ensuring all discs fit, which makes sense given the problem needs all discs stored.
Hence, the choice that matches the mathematical sentence needed to express how many boxes Crystal needs is:
Option D: [tex]\(16b \geq 94\)[/tex]
This inequality means we need enough boxes so that their total capacity (16 discs per box) meets or exceeds the total number of discs, 94. Using such boxes, Crystal will need 6 boxes to store all her discs.
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