To solve the equation \(17p + 4 = 55\), follow these steps:
- Subtract 4 from both sides to isolate the term with \(p\):
\[ 17p + 4 - 4 = 55 - 4 \]
\[ 17p = 51 \]
- Now, divide both sides by 17 to solve for \(p\):
\[ p = \frac{51}{17} \]
- Simplify the fraction:
\[ p = 3 \]
Thus, the value of the variable \(p\) is
\[ \boxed{3} \]