Mary Beth starts with $200 in her bank account. Every week she withdraws $15 for miscellaneous expenses. For how many weeks could she withdraw the money if she maintains a balance of at least $35?
Write an inequality to represent the situation. Use x to represent the number of weeks.


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 Each week, Mary Beth’s balance decreases by $15, so after $ x $ weeks, she will have withdrawn $ 15x $ dollars.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 Her remaining balance after $ x $ weeks will be her starting balance minus the total withdrawn: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.

Mary Beth starts with $200 in her bank account. Every week she withdraws $15 for miscellaneous expenses. For how many weeks could she withdraw the money if she maintains a balance of at least $35? Write an inequality to represent the situation. Use x to represent the number of weeks.

Explore how to solve the inequality 200 - 15x >= 35 to find how many weeks Mary Beth can withdraw $15 from her $200 bank account while maintaining a balance of at least $35. This problem introduces key algebraic concepts such as linear equations and inequalities, suitable for students in Grades 7-9.

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