In qualitative analysis, the metals of group I can be separated from other ions by precipitating them as chloride salts. A solution initially contains $Ag^+$ and $Pb^{2+}$ at a concentration of 0.10 M. Aqueous HCl is added to this solution until the $Cl^-$ concentration is 0.10 M. What will the concentrations of $Ag^+$ and $Pb^{2+}$ be at equilibrium? ($K_{sp}$ for AgCl = $1.8 \times 10^{-10}$, $K_{sp}$ for $PbCl_2$ = $1.7 \times 10^{-5}$)