https://file.aiquickdraw.com/mathbot/file/1726232596430qdf99sxq.jpg

Let's break down the problem step by step to solve it:

### Given:
- Anne earns $42 per hour.
- Her daily expense for dry cleaning is $75.
- She wants to earn more than $260 a day after covering her dry cleaning costs.

### Let:
- $ h $ be the number of hours she works.

### Total earnings:
Anne's total daily earnings are $ 42h $.

### Net earnings:
After deducting her daily expense of $75 for dry cleaning, her net earnings are $ 42h - 75 $.

### Condition:
She wants her net earnings to be more than $260, so we set up the inequality:
\[
42h - 75 > 260
\]

### Solve for $ h $:
1. Add 75 to both sides:
\[
42h > 335
\]

2. Divide both sides by 42:
\[
h > \frac{335}{42} \approx 7.98
\]

### Conclusion:
Anne must work at least 8 hours to meet her goal of making more than $260 a day.

Would you like further details or explanations on any part? Here are 5 related questions for deeper understanding:

1. What would be Anne's total earnings if she worked for exactly 8 hours?
2. How much would Anne earn if her dry cleaning cost increased to $100 per day?
3. What if Anne received a raise and started making $50 per hour—how would that affect her working hours to reach the goal?
4. How would her required hours change if her daily expense was reduced by 10%?
5. What if she wanted to make exactly $400 per day after covering dry cleaning expenses—how many hours would she need to work?

### Tip:
When solving inequalities, always remember to check your final solution by plugging it back into the original context to ensure it satisfies all conditions.

Anne works in New York City and makes $42 per hour. She works in an office and must get her suit dry cleaned every day for $75. If she wants to make more than $260 a day, at least how many hours must she work?

Learn how to solve a linear inequality problem involving wages and expenses. Anne works for $42 per hour and has daily dry cleaning costs of $75. This problem helps find the minimum hours she must work to earn more than $260 a day. Suitable for students in Grades 6-8.

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