Let's define the number Jill is thinking of as \( x \).
According to the problem, "Four more than three times the number is thirteen." We can express this as an equation:
\[ 3x + 4 = 13 \]
To find \( x \), we first subtract 4 from both sides of the equation:
\[ 3x + 4 - 4 = 13 - 4 \] \[ 3x = 9 \]
Next, we divide both sides by 3:
\[ x = \frac{9}{3} \] \[ x = 3 \]
Therefore, Jill's number is \( 3 \).