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Answer :
To solve the problem of determining how many boxes Crystal will need to store her 94 compact discs, we need to express the situation in a mathematical statement.
1. Understand the Problem:
- Crystal has a total of 94 compact discs.
- Each box can hold 16 discs.
2. Determine the Number of Boxes Needed:
- We want to find the minimum number of boxes required to store all 94 discs.
- Since each box holds 16 discs, we need to calculate how many groups of 16 can fit into 94.
3. Formulate the Mathematical Sentence:
- For each box, if `b` is the number of boxes needed, then the total capacity of `b` boxes must be at least 94 discs.
- Therefore, the mathematical inequality is: `16 * b ≥ 94`
- This means: "16 discs per box times the number of boxes is greater than or equal to 94 discs."
4. Choosing the Correct Option:
- Analyze the options given:
- A. [tex]\(16b < 94\)[/tex] – This suggests fewer discs than needed, which is incorrect.
- B. [tex]\(16b \geq 94\)[/tex] – This captures the exact need to ensure all discs fit.
- C. [tex]\(b + 16 = 94\)[/tex] – This inaccurately suggests adding 16 to the number of boxes, which isn't the requirement.
- D. [tex]\(94 - b = 16\)[/tex] – This suggests subtracting boxes from 94 discs, which doesn’t relate correctly.
5. Conclusion:
- The option that mathematically represents the situation is option B: [tex]\(16b \geq 94\)[/tex].
- This ensures that all the discs will be stored completely.
Thus, Crystal will need to ensure that the total capacity of the boxes meets at least 94 discs, represented correctly by option B.
1. Understand the Problem:
- Crystal has a total of 94 compact discs.
- Each box can hold 16 discs.
2. Determine the Number of Boxes Needed:
- We want to find the minimum number of boxes required to store all 94 discs.
- Since each box holds 16 discs, we need to calculate how many groups of 16 can fit into 94.
3. Formulate the Mathematical Sentence:
- For each box, if `b` is the number of boxes needed, then the total capacity of `b` boxes must be at least 94 discs.
- Therefore, the mathematical inequality is: `16 * b ≥ 94`
- This means: "16 discs per box times the number of boxes is greater than or equal to 94 discs."
4. Choosing the Correct Option:
- Analyze the options given:
- A. [tex]\(16b < 94\)[/tex] – This suggests fewer discs than needed, which is incorrect.
- B. [tex]\(16b \geq 94\)[/tex] – This captures the exact need to ensure all discs fit.
- C. [tex]\(b + 16 = 94\)[/tex] – This inaccurately suggests adding 16 to the number of boxes, which isn't the requirement.
- D. [tex]\(94 - b = 16\)[/tex] – This suggests subtracting boxes from 94 discs, which doesn’t relate correctly.
5. Conclusion:
- The option that mathematically represents the situation is option B: [tex]\(16b \geq 94\)[/tex].
- This ensures that all the discs will be stored completely.
Thus, Crystal will need to ensure that the total capacity of the boxes meets at least 94 discs, represented correctly by option B.
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