In one week in , a technician earned a total of $ by working at her regular job and at a second job doing part-time work. The equation represents this situation, where is the number of hours worked at her regular job and is the number of hours worked at her second job. Which of the following is the best interpretation of in this context?
Explanation
Answer: A. The amount, in dollars, the technician earned for each hour she worked at her regular job
Explanation:1. Given Information: In one week, a technician earned a total of $. Equation representing the situation: . = number of hours worked at her regular job. = number of hours worked at her second job. We need to interpret the meaning of in this context.
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Analyze the Equation Structure: The equation is a sum of two terms equaling the total earnings: Term 1: Term 2: Total Earnings:
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Interpret Term 1 (): This term represents the total earnings from the regular job. It is a product of the number and (the number of hours worked at the regular job). For the product to represent earnings in dollars, and to be in hours, the coefficient must represent the rate of earnings in dollars per hour for the regular job. So, is the hourly wage (in dollars) for the regular job.
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Interpret Term 2 () (for completeness): Similarly, represents the total earnings from the second job. Since is the number of hours worked at the second job, must be the hourly wage (in dollars) for the second job.
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Compare with Options: [A] The amount, in dollars, the technician earned for each hour she worked at her regular job - This matches our interpretation of . [B] The amount, in dollars, the technician earned for each hour she worked at her second job - This would be represented by . [C] The number of hours the technician worked in one week at her regular job - This is represented by . [D] The number of hours the technician worked in one week at her second job - This is represented by .
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Conclusion: The best interpretation of in this context is the amount, in dollars, the technician earned for each hour she worked at her regular job.