Tomás starts with $20 in his bank account. Every week, he deposits $60. For how many weeks might he have been depositing money if his account balance is now at least $440?

We are given that Tomás starts with $20 in his bank account and deposits $60 each week. We need to determine for how many weeks he might have been depositing money if his account balance is now at least $440.

### Step 1: Formulate an equation
Let $ x $ represent the number of weeks Tomás has been depositing money. The total amount in his account after $ x $ weeks can be expressed as:

\[
\text{Account balance} = 20 + 60x
\]

We are told that his account balance is at least $440, so we set up the inequality:

\[
20 + 60x \geq 440
\]

### Step 2: Solve the inequality
Now, solve for $ x $:

\[
60x \geq 440 - 20
\]

\[
60x \geq 420
\]

\[
x \geq \frac{420}{60}
\]

\[
x \geq 7
\]

### Step 3: Interpretation
Tomás must have been depositing money for **at least 7 weeks** for his account balance to be at least $440.

Would you like further clarification on this solution?

Here are five related questions:
1. How much money will Tomás have after 10 weeks?
2. What is the equation for Tomás' account balance if he starts with a different amount, say $50?
3. If Tomás withdraws $30 every other week, how does that change the equation?
4. How long would it take for Tomás' balance to reach exactly $1,000?
5. What if Tomás makes an initial deposit of $100 instead of $20?

**Tip:** Inequalities often represent real-world constraints, like "at least" or "no more than" limits.

Learn how to solve the inequality involving Tomás' weekly deposits to determine how many weeks he needs to save to have at least $440. This problem involves algebraic concepts such as inequalities and linear equations, suitable for Grades 6-8.

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