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The problem presented asks for an inequality that represents the situation where the amount of money in Bianca’s account is less than the amount of money in Stephen’s account.

### Information given:
- **Bianca's account:**
  - Started with $500.
  - Deposited $20 per week for $ x $ weeks.
  - Total money after $ x $ weeks: $ 500 + 20x $.

- **Stephen's account:**
  - Started with $0.
  - Deposited $60 per week for $ x $ weeks.
  - Total money after $ x $ weeks: $ 60x $.

The problem asks for an inequality where the amount in **Bianca's account** is **less than** the amount in **Stephen's account**.

So, we are comparing the two expressions:
\[
500 + 20x \text{ (Bianca's account)} < 60x \text{ (Stephen's account)}.
\]

### Setting up the inequality:
\[
500 + 20x < 60x.
\]

Now, simplify the inequality:
1. Subtract $ 20x $ from both sides:
   \[
   500 < 40x.
   \]

2. Divide both sides by 40:
   \[
   \frac{500}{40} < x \quad \Rightarrow \quad 12.5 < x.
   \]

Thus, the correct inequality is $ 500 + 20x < 60x $, which corresponds to **Option C**.

### Answer: C $ 60x > 500 + 20x $.

Would you like a more detailed explanation, or do you have any other questions?

### Related questions:
1. How would the inequality change if Bianca deposited $30 per week?
2. If Stephen deposited $50 per week, what would the new inequality look like?
3. At what point, $ x $, will the two accounts have the same balance?
4. How much more does Stephen deposit each week compared to Bianca?
5. How would the inequality change if both accounts earned interest?

### Tip:
Always align the terms of inequalities on one side to simplify solving and interpreting the inequality.

Bianca had $500 in her checking account when Stephen opened a checking account with $0. Bianca deposited $20 into her account each week for x weeks. Stephen deposited $60 into his account each week for x weeks. The accounts did not earn interest. Which inequality represents this situation when the amount of money in Bianca’s account is less than the amount of money in Stephen’s account?

Learn how to set up and solve an inequality to compare the amount of money in two accounts. Bianca starts with $500 and deposits $20 weekly, while Stephen starts at $0 but deposits $60 weekly. Suitable for Grades 6-8, this problem covers inequalities and basic algebraic manipulation.

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