An improved formulation of the extension of the statistical associating fluid theory for potentials of variable range to electrolytes (SAFT-VRE) is presented, incorporating a representation for the dielectric constant of the solution that takes into account the temperature, density and composition of the solvent. The proposed approach provides an excellent correlation of the dielectric-constant data available for a number of solvents including water, representative alcohols and carbon dioxide, and it is shown that the methodology can be used to treat mixed-solvent electrolyte solutions. Models for strong electrolytes of the metal-halide family are considered here. The salts are treated as fully dissociated and ion-specific interaction parameters are presented. Vapour pressure, density, and mean ionic activity coefficient data are used to determine the ion–ion and solvent–ion parameters, and mixed-salt electrolyte solutions (brines) are then treated predictively. We find that the resulting intermolecular potential models follow physical trends in terms of energies and ion sizes with a close relationship observed with well-established ionic diameters. A good description is obtained for the densities, mean ionic activity coefficients, and vapour pressures of the electrolyte solutions studied. The theory is also seen to provide excellent predictions of the osmotic coefficient and of the depression of the freezing temperature, and provides a qualitative estimate of the solvation free energy. The vapour pressure of aqueous brines is predicted accurately, as is the density of these solutions, although not at the highest pressures considered. Calculations for the vapour–liquid and liquid–liquid equilibria of salts in water+methanol and water+n-butan-1-ol are presented. In addition, it is shown that the salting-out of carbon dioxide in sodium chloride solutions is captured well using a predictive model.