$(10$ pts$)$ Points $1$ and $2$ have elevations of $6$ ft and $10$ ft $,$ respectively, above a vertical datum as shown. $P_1$ was measured as $400$ psf and $P_2$ was measured as $75$ psf$.$ Determine the density $($slug$/$ft ${?}^3)$ and specific weight $(l\frac{b}{f}{t}^3)$ of the fluid.