  We present a continuum theory of electrolytes composed of a waterlike solvent
and univalent ions. First, we start with a density functional $\cal F$ for the
coarse-grained solvent, cation, and anion densities, including the
Debye-H\"uckel free energy, the Coulombic interaction, and the direct
interactions among these three components. These densities fluctuate obeying
the distribution $\propto \exp(- {\cal F}/k_BT)$. Eliminating the solvent
density deviation in $\cal F$, we obtain the effective non-Coulombic
interactions among the ions, which consist of the direct ones and the
solvent-mediated ones. %where the latter are written in terms of the ion
volumes %and are inversely proportional to the solvent compressibility. We then
derive general expressions for the ion correlation, the apparent partial
volume, and the activity and osmotic coefficients up to linear order in the
average salt density $n_{\rm s}$. Secondly, we perform numerical analysis using
the Mansoori-Carnahan-Starling-Leland model $[$J. Chem. Phys. {\bf 54}, 1523
(1971)$]$ for three-component hardspheres. The effective interactions
sensitively depend on the cation and anion sizes due to competition between the
steric and hydration effects, which are repulsive between small-large ion pairs
and attractive between symmetric pairs. These agree with previous experiments
and Collins' rule $[$Biophys. J. {\bf 72}, 65 (1997)$]$. We also give simple
approximate expressions for the ionic interaction coefficients valid for any
ion sizes.
