Pregunta
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()) A mechanic named Farid plans to work a maximum of 9 hours tomorrow, and no \( m \) oing tune-ups and oil changes. It takes 1 hour to perform a tune-up and 2 hours to pe oll change. d) Write the inequality in standard form that describes this situation. Use the given umbers and the following variables. 4) \( x= \) the number of tune-ups (1) \( y= \) the number of oil changes \( > \)

Ask by Chandler Dawson. in the United States
Feb 09,2025

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The inequality is \( x + 2y \leq 9 \).

Solución

To formulate the inequality that describes Farid's work situation, we need to consider the following: 1. **Variables:** - Let \( x \) be the number of tune-ups. - Let \( y \) be the number of oil changes. 2. **Time Constraints:** - Each tune-up takes 1 hour, so \( x \) tune-ups will take \( x \) hours. - Each oil change takes 2 hours, so \( y \) oil changes will take \( 2y \) hours. - Farid plans to work a maximum of 9 hours. 3. **Inequality:** - The total time spent on tune-ups and oil changes must be less than or equal to 9 hours. Therefore, we can express this as: \[ x + 2y \leq 9 \] This inequality represents the maximum time Farid can spend on tune-ups and oil changes combined. Thus, the inequality in standard form is: \[ x + 2y \leq 9 \]

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Beyond the Answer

Farid's work hours can be represented with the inequality \( x + 2y \leq 9 \). Here, \( x \) is the number of tune-ups (each taking 1 hour) and \( y \) is the number of oil changes (each taking 2 hours). This means that the total time spent on tune-ups and oil changes cannot exceed 9 hours. In practical terms, this inequality helps Farid plan his day efficiently based on how many vehicles he can service. If he spends time doing more tune-ups, he will have less time for oil changes, and vice versa. This way, he can maximize his productivity while staying within his time constraints!

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