Answer
See solution below
Work Step by Step
$m_{fat}=mf=V_{fat}\delta_{fat}$
$m_{fat free}=m(1-f)=V_{fat free}\delta_{fat free}$
$\delta_w=X\delta_f=\frac{m_t}{V_t}=\frac{m_{fat}+m_{fat free}}{V_{fat}+V_{fat free}}=\frac{1}{\frac{f}{\delta_{fat}}+\frac{1-f}{\delta_{fat free}}}$
$f=\frac{\delta_{fat}\delta_{fat free}}{X\delta_w(\delta_{fat free}-\delta_{fat})}-\frac{\delta_{fat}}{\delta_{fat free}-\delta_{fat}}=
\frac{(0.90\frac{g}{cm^3})(1.10\frac{g}{cm^3})}{X(1.00\frac{g}{cm^3})((0.90\frac{g}{cm^3})-(1.10\frac{g}{cm^3}))}-\frac{(0.90\frac{g}{cm^3})}{(1.10\frac{g}{cm^3})-(0.90\frac{g}{cm^3})}$
$\%$ Body fat $=100f=\frac{495}{X}-450$