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Let's solve this step by step.

Ahmed starts with a wage of $7.50 per hour and gets a raise of $0.25 every 6 months. This means the sequence of his hourly wages will increase by $0.25 every term. So the sequence starts at $7.50, and each subsequent term will be $0.25 higher than the previous one.

Here is the sequence based on this setup:

- Start: $7.50
- After 6 months: $7.50 + $0.25 = $7.75
- After another 6 months: $7.75 + $0.25 = $8.00
- After another 6 months: $8.00 + $0.25 = $8.25
- After another 6 months: $8.25 + $0.25 = $8.50
- And so on...

Now, let's look at the answer choices:

- **A**: This sequence increases too quickly.
- **B**: This sequence shows the correct pattern: 7.75, 8.00, 8.25, 8.50, etc.
- **C**: These numbers do not represent hourly wages.
- **D**: This matches the correct values.
- **E**: This is a decreasing sequence, which doesn’t fit the problem.

The correct answer is **B**, as it reflects a gradual increase of $0.25 every 6 months.

Do you want more details or have any other questions?

Here are 5 related questions to explore:

1. How would the sequence change if the raise was $0.50 per hour every 6 months?
2. What would be Ahmed’s hourly wage after 3 years of working?
3. How many years would it take for Ahmed’s hourly wage to reach $10.00?
4. What is the sum of Ahmed’s hourly wages over the first two years of work?
5. How would the sequence change if Ahmed’s starting wage was $8.00 instead of $7.50?

**Tip**: Always identify the rate of change and apply it consistently to see if patterns match a sequence.

Ahmed is working at a burger joint. His boss pays him $7.50 per hour and promises a raise of $0.25 per hour every 6 months. Which sequence describes Ahmed's expected hourly wages, in dollars, starting with his current wage?

Learn how to determine the expected hourly wages in an arithmetic sequence, starting from $7.50 per hour with a raise of $0.25 every six months. This problem covers key arithmetic concepts and is suitable for middle school students (Grades 6-8).

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