Let's define the situation step by step and translate it into an inequality.

Variables and constants:

• Mary Beth starts with $200.
• Each week, she withdraws $15.
• She wants to maintain a balance of at least $35 in her account.
• Let $x$ represent the number of weeks.

Step-by-step translation:

1. Each week, Mary Beth’s balance decreases by $15, so after $x$ weeks, she will have withdrawn $15x$ dollars.
2. Her remaining balance after $x$ weeks will be her starting balance minus the total withdrawn: $200 - 15x$
3. She wants this balance to be at least $35, so the inequality is: $200 - 15x \geq 35$

Solving the inequality:

1. Subtract 200 from both sides: $-15x \geq 35 - 200$ $-15x \geq -165$
2. Divide both sides by -15 (remember to reverse the inequality sign because we are dividing by a negative number): $x \leq \frac{-165}{-15}$ $x \leq 11$

Conclusion:

Mary Beth can withdraw money for up to 11 weeks while maintaining a balance of at least $35.

Would you like further details or have any questions about this?

Here are 5 related questions:

1. How much money will Mary Beth have after 8 weeks of withdrawals?
2. What happens if she increases her weekly withdrawal to $20? How many weeks can she maintain a balance of $35?
3. If her starting balance was $300 instead of $200, how many weeks could she withdraw $15?
4. What if she wanted to maintain a balance of $50 instead of $35?
5. If she deposits $10 every 3 weeks, how will this affect the number of weeks she can withdraw?

Tip: In inequalities, remember to reverse the inequality sign when multiplying or dividing by a negative number.