Let's solve the problem step by step:

Given Information:

• Payment for $21 \frac{1}{2}$ hours (which is 21.5 hours) = $232.39
• Required payment for 33 hours.

Step 1: Calculate the hourly rate.

$\text{Hourly Rate} = \frac{232.39}{21.5} \approx 10.81$

Step 2: Calculate payment for 33 hours.

$\text{Total Payment} = 10.81 \times 33 \approx 356.73$

Final Answer:

You should be paid $356.73 for 33 hours of work.

Would you like a detailed explanation or have any questions?

Here are five related questions to expand your understanding:

1. How do you convert a mixed number to a decimal?
2. How do you calculate proportional relationships in wage problems?
3. How do rounding rules affect wage calculations?
4. What are some real-world applications of hourly rate calculations?
5. How can you verify your calculations using unit rates?

Tip: Always double-check unit conversions when working with fractional hours.