Based on generalized van der Waals partition function theory and approximations of radial distribution functions, mixing rules for the attractive part of an equation of state have been presented for extension of an augmented hard-core equation of state to mixtures. Two approximations, the van der Waals one-fluid approximation and the mean density approximation, are applied in this study. Within the framework of the conformal solution theory, the properties of a hypothetical fluid were calculated from the attractive part of an augmented hard-core equation of state. As a preliminary test of the method, an augmented hard-sphere equation of state has been applied. For polar systems in which components do not differ appreciably in size, both the MDA and the VDW models yield satisfactory results for the vapor-liquid equilibrium calculations. However, for strongly non-ideal fluid systems, the MDA is superior to the VDW. Adopting the mixing rules for the repulsive hard-core mixtures to describe structure effects, the proposed method can, in principle, be used to extend any accurate augmented hard-core equation of state to mixtures.