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The problem asks for an inequality that can determine the number of days until Brandon has more money than Dylan. 

### Let’s break down the problem:
- **Brandon** starts with **$350** and earns **$35 per day**.
- **Dylan** starts with **$400** and earns **$25 per day**.

We can set up an equation to represent each person's total money after $ x $ days:
- Brandon's money after $ x $ days: $ 350 + 35x $
- Dylan's money after $ x $ days: $ 400 + 25x $

We want to find when Brandon has **more money than Dylan**, so we need an inequality:
\[
350 + 35x > 400 + 25x
\]

Now, let’s simplify the inequality:

1. Subtract $ 25x $ from both sides:
\[
350 + 10x > 400
\]

2. Subtract 350 from both sides:
\[
10x > 50
\]

3. Finally, divide by 10:
\[
x > 5
\]

So, Brandon will have more money than Dylan after **5 days**.

### Correct Inequality:
The inequality that matches the given options is:
\[
350 + 35x > 400 + 25x
\]

### This corresponds to the third option.

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Would you like further details or have any additional questions?

Here are some related questions:
1. How would the inequality change if Brandon earned $40 per day instead?
2. What if Dylan started with $450 instead of $400?
3. How would the solution change if Brandon started with $300?
4. What if both Brandon and Dylan earned the same amount per day?
5. How can this problem be represented graphically?

**Tip:** Always make sure to balance both sides of the inequality carefully when solving for a variable.

Brandon has $350 in his account and is earning $35 a day. Dylan has $400 in his account and earns $25 a day. Which inequality can be used to determine the number of days until Brandon has more money than Dylan?

Learn how to solve a linear inequality comparing Brandon and Dylan's savings. Brandon starts with $350 and earns $35 per day, while Dylan starts with $400 and earns $25 per day. This problem explores algebraic concepts such as inequalities and linear equations. Suitable for students in Grades 6-8.

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