Question
()) 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
Upstudy AI Solution
Tutor-Verified Answer
Answer
The inequality is \( x + 2y \leq 9 \).
Solution
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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Simplify this solution 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!
