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.