We present results on the thermodynamic and structural aspects of the hydration of hydrophobic solutes in three tetramethylammonium [N(CH3)(4)(+)] Salt solutions at various concentrations obtained from molecular dynamics simulations. Monovalent counterions of different sizes-F-, Cl-, and a relatively large model ion BI--are chosen in order to cover a range of kosmotropic to chaotropic behaviors. Chemical potentials of hard-sphere solutes obtained using test particle insertions display both salting-in and salting-out effects depending on the type of salt. Water and salt-ion densities in the vicinity of hard-sphere solutes are calculated. Small and strongly hydrated F- ions (kosmotropes) are excluded from the vicinity of hydrophobic solutes, leading to an increase in local water densities near hydrophobic solutes (i.e., preferential hydration). This increases the excess chemical potential of hydrophobic solutes in solution which leads to salting-out. Opposite behavior is observed for large, less favorably hydrated BI- ions (chaotropes) which associate strongly with hydrophobic solutes. Compressive forces due to neighboring water molecules, cations, and anions on the surface of the hard sphere solute are calculated. We find that water molecules make the most significant contribution toward the total compressive force. This explains the observed linear correlation between the extent of preferential hydration or dehydration of the solute surface and salting-out or salting-in effects. The trends in the thermodynamics of hydration of hydrophobic solutes upon addition of salts are explained in terms of the structural hydration of individual salt ions.