The problem asks which inequality shows the number of weeks ($w$) needed to save at least $535 for a trip, given that $200 is already saved and $25 is saved per week.

Breaking it down:

• Total savings goal: $535$
• Already saved: $200$
• Savings per week: $25$

The correct inequality must reflect that the total savings (from the already saved $200 plus $25 per week) must be at least $535$, meaning:

$25w + 200 \geq 535$

Correct answer: The second option ($25w + 200 \geq 535$) is correct.

Let me know if you'd like further clarification or help solving inequalities! Here are five related questions to expand your understanding:

1. How would you solve $25w + 200 \geq 535$ to find the minimum $w$?
2. What does the inequality $25w + 200 \leq 535$ represent in this scenario?
3. What happens if the weekly savings increase to $30? How would the inequality change?
4. If only $100 was initially saved, how would the inequality change?
5. How would this situation differ if you needed to save exactly $535, not at least?

Tip: When dealing with inequalities, always carefully interpret the context to determine whether it's a “greater than or equal to” or a “less than or equal to” scenario.