A machine makes -inch, -inch, and -inch parts. During a certain day, the number of -inch parts that the machine makes is times the number of -inch parts, and the number of -inch parts is . During this day, the machine makes parts total. Which equation represents this situation?
Explanation
Answer: D.
Explanation:1. **Understand the problem and define variables:** We need to create an equation representing the total number of parts made. * Let be the number of -inch parts. * Number of -inch parts = (given as times the number of -inch parts). * Number of -inch parts = (given). * Total number of parts = (given).
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**Set up the equation for the total number of parts:** The total number of parts is the sum of the number of parts of each size. Total parts = (Number of -inch parts) + (Number of -inch parts) + (Number of -inch parts)
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**Substitute the expressions for each quantity:**
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**Simplify the equation:** Combine the terms with : So, the equation becomes: This can also be written as:
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**Compare with the given options:** The derived equation matches option D. Options A and B incorrectly incorporate the sizes of the parts (-inch, -inch, -inch) as coefficients for the *number* of parts in an equation for the *total number* of parts. Option C omits the number of -inch parts.
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**Conclusion:** The equation that represents this situation is .