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.