Step 1: Set up the inequality. Let $B_0$ be the initial bank balance, $W$ be the weekly withdrawal amount, and $n$ be the number of weeks. The balance after $n$ weeks is $B_0 - n \times W$. Anna wants to maintain a balance of at least Tshs 200,000. $$B_0 - n \times W \ge 200,000$$ Given: $B_0 = \text{Tshs } 500,000$ $W = \text{Tshs } 40,000$ Substitute the values into the inequality: $$500,000 - n \times 40,000 \ge 200,000$$ Step 2: Isolate the term with $n$. Subtract 500,000 from both sides: $$-n \times 40,000 \ge 200,000 - 500,000$$ $$-n \times 40,000 \ge -300,000$$ Step 3: Solve for $n$. Divide both sides by -40,000. Remember to reverse the inequality sign when dividing by a negative number: $$n \le \frac{-300,000}{-40,000}$$ $$n \le \frac{30}{4}$$ $$n \le 7.5$$ Step 4: Interpret the result. Since $n$ represents the number of weeks, it must be a whole number. Anna can withdraw money for a maximum of 7 full weeks while maintaining a balance of at least Tshs 200,000. If she withdraws for 8 weeks, her balance will fall below Tshs 200,000. The maximum number of weeks she can withdraw money is $\boxed{\text{7 weeks}}$.