To calculate how much the customer will owe the painter, follow these steps:

1. Calculate the area of the room: The dimensions of the room are $12 \frac{1}{2}$ feet by 15 feet. First, convert $12 \frac{1}{2}$ to an improper fraction or decimal: $12 \frac{1}{2} = 12.5 \text{ feet}.$ Now, multiply the two dimensions to find the area: $\text{Area} = 12.5 \times 15 = 187.5 \text{ square feet}.$

2. Calculate the total cost: The painter charges $3.25 per square foot. To find the total cost, multiply the area by the rate: $\text{Total cost} = 187.5 \times 3.25 = 609.375.$

3. Final amount: The customer will owe the painter $609.38 (rounded to two decimal places).

Would you like further details or explanations on any part?

Here are 5 related questions to expand your understanding:

1. How would the cost change if the painter charged $4.00 per square foot?
2. What if the dimensions of the room were in meters instead of feet?
3. How much would the painter charge for a room with a triangular shape?
4. What would the cost be if the room had two walls not being painted?
5. How do material costs affect the overall painting fee?

Tip: Always convert mixed numbers to decimals or improper fractions for easier multiplication.