To determine the number of gallons of water for which Judy was charged, we need to set up an equation based on the given information.

The total amount of Judy's water bill is $40.50. This bill consists of a fixed charge of $13.50 plus a charge of $0.0075 per gallon for the water used.

Let $g$ be the number of gallons of water used. The equation for the total bill can be expressed as:

$\text{Total bill} = \text{Fixed charge} + (\text{Charge per gallon} \times \text{Number of gallons})$

Substituting the given values into the equation:

$40.50 = 13.50 + 0.0075g$

To find $g$, first subtract the fixed charge from the total bill:

$40.50 - 13.50 = 0.0075g$

$27.00 = 0.0075g$

Next, solve for $g$ by dividing both sides of the equation by 0.0075:

$g = \frac{27.00}{0.0075}$

Calculating the division:

$g = \frac{27.00}{0.0075} = 3600$

Therefore, Judy was charged for 3600 gallons of water.

The answer is: $\boxed{3600}$

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. What would Judy’s water bill be if she used 4500 gallons in a quarter?
2. How much would the total bill be if the fixed charge was increased to $15?
3. If the charge per gallon increased to $0.01, what would the total bill be for 3600 gallons?
4. How many gallons would Judy use if her bill was $50?
5. What is the percentage increase in the bill if Judy uses 5000 gallons instead of 3600 gallons?
6. How much would Judy save if she used 3000 gallons instead of 3600 gallons?
7. What is the total amount billed if Judy doesn't use any water at all?
8. How many gallons would result in a total bill of $100?

Tip: When solving linear equations involving costs and rates, clearly identify the fixed and variable components to set up the equation accurately.