A new approach for obtaining mixture properties is proposed. It involves combining recently derived exact equations relating integrals of the mixture pair correlation functions with approximate closures. A partial differential equation for the partition function results. This equation is integrated using an appropriately selected initial condition. The procedures are illustrated for additive and nonadditive hard spheres, and new mixture equations are obtained. Comparison with simulation data show that the accuracy of the predicted properties depends on the level of approximation introduced by the closure. Certain mixture equations gave accurate representation of the equation of state and the phase boundaries of nonadditive hard spheres. In applications where the structure of the fluid is not needed, the proposed approach is better than traditional approaches, because it gives accurate analytical expressions for mixture properties and for certain integrals of the pair correlation functions. (C) 1997 American Institute of Physics. [S0021-9606(97)50941-X].