We have developed robust and very efficient algorithms for solving the reference interaction site model (RISM) equations for salt solutions in the bulk and near a solute atom of noble gases. The theory of dielectric consistency recently developed for solutions at finite salt concentrations is employed in the formalism. The change in water structure in the bulk caused by addition of salts have been examined for model 1-1 salt solutions (LiCl, NaCl, KCl, KF, KBr, KI, and CsI). The density and orientational structures of each salt solution near a solute atom have been analyzed. The water model employed is the extended simple point charge (SPC/E) model. Ions characterized by positive hydration (F-, Li+, and Na+) are strongly hydrated in the bulk and stay significantly far from the atom. Those of negative hydration (Cl- and Br-) or hydrophobic hydration (Cs+ and I-) are excluded from the bulk to the atom. Due to a specific orientational order of water molecules adjacent to the solute atom, there is a trend that cations stay less closer to the atom than anions. Overall, cations indirectly affect the solubility of noble gases via the change in water structure induced by addition of those ions. On the other hand, anions affect the solubility not only indirectly but also directly by interacting with solute atoms. The agreement between the calculated and experimental values for the salting coefficient is excellent for He. However, the discrepancy becomes larger as the number of electrons of the solute atom increases (the calculated value is larger), which implies that the ion-induced dipole interaction neglected has significantly large effects.