Answer
The center of mass is a distance of 2520 km from the center of Pluto.
Work Step by Step
We can find the ratio of Pluto's radius to Charon's radius.
$\frac{1185~km}{625~km} = 1.896$
Let $m_c$ be the mass of Charon. Since $mass \propto r^3$, Pluto's mass $m_p = (1.896)^3~m_c$, which is $6.816\times m_c$
Let the center of Pluto be at the origin.
$x_{cm} = \frac{m_px_p+m_cx_c}{m_p+m_c}$
$x_{cm} = \frac{0+m_c~(19700~km)}{6.816\times m_c+m_c}$
$x_{cm} = 2520~km$
The center of mass is a distance of 2520 km from the center of Pluto.
