Cecilia starts with $10 in her bank account. Every week, she deposits $50. For how many weeks might she have been depositing money if her account balance is now at least $410?

Let's break down the problem:

Cecilia starts with $10 in her bank account, and every week she deposits $50. We want to determine how many weeks of deposits would result in her account balance being at least $410.

### Step 1: Express the situation mathematically.
After $ n $ weeks, Cecilia will have deposited $ 50n $ dollars in addition to her initial $10. Therefore, her total balance after $ n $ weeks is:

\[
\text{Balance} = 50n + 10
\]

We know that her balance is at least $410, so we can write the inequality:

\[
50n + 10 \geq 410
\]

### Step 2: Solve the inequality.

Subtract 10 from both sides:

\[
50n \geq 400
\]

Now, divide both sides by 50:

\[
n \geq 8
\]

### Conclusion:
Cecilia has been depositing money for at least **8 weeks** for her balance to reach or exceed $410.

Would you like more details or explanations on any step?

Here are 5 related questions:
1. What would Cecilia’s balance be after 12 weeks of deposits?
2. How much money does she need to deposit to reach $1,000?
3. If she stops depositing money after 10 weeks, what will her balance be?
4. If she withdraws $20 every 3 weeks, how does that affect the balance?
5. How much time would it take her to double her balance after reaching $410?

**Tip:** To solve inequalities involving word problems, first translate the scenario into a mathematical expression and then solve as you would with equations.

Learn how to solve the linear inequality where Cecilia deposits $50 weekly starting with $10. Find out how many weeks it takes for her bank balance to reach at least $410. Ideal for Grades 6-8, this solution covers algebra and inequalities.

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