We propose a simple model to explain the nonmonotonic concentration dependence of the mean activity coefficient of simple electrolytes without using any adjustable parameters. The primitive model of electrolytes is used to describe the interaction between ions computed by the adaptive grand canonical Monte Carlo method. For the dielectric constant of the electrolyte, we use experimental concentration dependent values. This is included through a solvation term in our treatment to describe the interaction between ions and water that changes as the dielectric constant changes with concentration. This term is computed by a Born-treatment fitted to experimental hydration energies. Our results for LiCl, NaCl, KCl, CsCl, NaBr, NaI, MgCl(2), CaCl(2), SrCl(2), and BaCl(2) demonstrate that the principal reason of the nonmonotonic behavior of the activity coefficient is a balance between the solvation and ion-ion correlation terms. This conclusion differs from previous studies that assumed that it is the balance of hard sphere repulsion and electrostatic attraction that produces the nonmonotonic behavior. Our results indicate that the earlier assumption that solvation can be taken into account by a larger, "solvated" ionic radius should be reconsidered. To explain second order effects (such as dependence on ionic size), we conclude that explicit water models are needed.