Hailey had $330 in her savings account when Darius opened a savings account with zero dollars.

• Hailey deposited $30 into her account each week for x weeks.
• Darius deposited $50 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 Hailey’s account was greater than the amount of money in Darius’s account?
A.30x < 330 + 50x
B.50x > 330 + 30x
C.30x > 330 + 50x
D.50x < 330 + 30x

To solve this problem, we need to compare the amount of money in Hailey's and Darius's accounts after they have been depositing money for $ x $ weeks.

**Hailey's account:**
- Initial amount: $330
- Weekly deposit: $30
- Total after $ x $ weeks: $ 330 + 30x $

**Darius's account:**
- Initial amount: $0
- Weekly deposit: $50
- Total after $ x $ weeks: $ 50x $

We are given that the amount of money in Hailey's account was greater than the amount of money in Darius's account. This leads to the inequality:

\[
330 + 30x > 50x
\]

Now, let's solve this inequality:

1. Subtract $ 30x $ from both sides:
   \[
   330 > 50x - 30x
   \]
   \[
   330 > 20x
   \]

2. Divide both sides by 20:
   \[
   \frac{330}{20} > x
   \]
   \[
   16.5 > x
   \]

So, the solution to the inequality is $ x < 16.5 $, meaning Hailey's account will have more money than Darius's as long as the number of weeks is less than 16.5.

Thus, the inequality that correctly represents this situation is:

\[
\boxed{D. \ 50x < 330 + 30x}
\]

Would you like further details on any steps, or do you have questions? Here are 5 related questions to expand on this information:

1. What happens after $ x $ reaches 16.5 weeks?
2. How would the situation change if Darius deposited more per week?
3. Can we use a graph to represent this inequality?
4. How would interest affect this comparison between their savings?
5. What happens if Hailey starts with more than $330?

**Tip:** When comparing two quantities that change over time, it's often helpful to set up an inequality and solve it to see when one will be larger than the other.

Hailey had $330 in her savings account when Darius opened a savings account with zero dollars. Hailey deposited $30 into her account each week for x weeks. Darius deposited $50 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 Hailey’s account was greater than the amount of money in Darius’s account? A.30x < 330 + 50x B.50x > 330 + 30x C.30x > 330 + 50x D.50x < 330 + 30x

Explore how to solve an inequality problem involving savings account balances. Hailey starts with $330 and deposits $30 weekly, while Darius deposits $50 weekly. Find out which inequality correctly represents when Hailey's account has more money. Suitable for students in Grades 6-8.

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