We have solved the Ornstein-Zernike equation in the hypernetted chain (HNC) approximation for several mixtures of electrolytes and uncharged hard spheres. The mixtures that we studied range from a simple restricted primitive model plus hard spheres of the same size to highly asymmetric electrolytes plus hard spheres of different sizes. We monitored the radial distribution function and thermodynamic properties. We find that the presence of neutral particles changes the nature pf the interaction between the charged particles. We also find a strong correlation between nonelectrostatic and electrostatic contributions to the free energy of the mixtures. Potential applications of this approach to the study of protein solubility in solutions of nonionic polymers are discussed.