To model the problem, we can use the equation:
\[ 15p = 540 \]
where \( p \) represents the cost of each piano lesson, and 15 is the number of lessons Brendan purchased, resulting in a total cost of $540.
Now, let's solve for \( p \):
\[ p = \frac{540}{15} \]
Calculating the right side:
\[ p = 36 \]
Thus, the cost of each piano lesson is \($36\).