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The question you have provided states that the relationship between the number of hours a plumber works and the total fee charged is proportional. The plumber charges $350 for 5 hours of work. You are asked to find which combinations of hours and fees listed are proportional to this rate.

Let's determine the plumber's hourly rate by dividing the total fee by the number of hours:

\[
\text{Hourly Rate} = \frac{350}{5} = 70 \, \text{dollars per hour}.
\]

Now, using this rate of $70 per hour, we'll calculate the total charge for the hours given in each option and see if they match the fee mentioned.

- **A: 3 hours**
  \[
  3 \times 70 = 210 \, (\text{not } 270)
  \]
  This does not match.

- **B: 3.5 hours**
  \[
  3.5 \times 70 = 245 \, (\text{matches 245})
  \]
  This matches.

- **C: 6 hours**
  \[
  6 \times 70 = 420 \, (\text{matches 420})
  \]
  This matches.

- **D: 7.25 hours**
  \[
  7.25 \times 70 = 507.50 \, (\text{matches 507.50})
  \]
  This matches.

- **E: 8 hours**
  \[
  8 \times 70 = 560 \, (\text{not } 490)
  \]
  This does not match.

### Correct answers:
- B: 3.5 hours and $245
- C: 6 hours and $420
- D: 7.25 hours and $507.50

Would you like a deeper explanation of proportional relationships or have any other questions? 

Here are 5 related questions for practice:
1. What is the formula for calculating the total fee based on hours worked and hourly rate?
2. If the plumber worked 10 hours, how much would she charge?
3. How does the concept of proportional relationships apply in other real-life situations?
4. If the rate changed to $80 per hour, how would the correct answers change?
5. How can you solve for the number of hours worked if only the total fee is given?

**Tip:** In proportional relationships, always check the constant ratio by dividing quantities to see if they hold consistently across different examples.

The relationship between the number of hours a plumber works and the total work fee she charges is proportional. Her fee for 5 hours of work is $350. Which of the following could be combinations of values for the plumber's work hours and total work fee she charges?

Learn how to solve a proportional relationship problem where a plumber charges $350 for 5 hours of work. Explore how to calculate fees for different work hours based on a fixed hourly rate. This problem covers key concepts such as rates, ratios, and proportionality, suitable for students in Grades 6-8.

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