We have applied the lattice Born-Green-Yvon theory to the study of hydrocarbon mixtures. In doing so we have fit pure component data in order to determine characteristic parameters for the pure fluids and have used the geometric mean approximation for the mixed-segment interaction energy. As a result, we have been able to make predictions for a nide variety of solution properties without fitting any data on the mixtures and have compared our predictions with experimental results. For binary alkane solutions made from combinations of n-hexane, n-octane, n-decane, and n-hexadecane we have found excellent agreement between theory and experiment for pressure-volume isotherms, volume changes on mixing and its pressure dependence, and equilibrium solution vapor pressures as a function of composition and temperature. For polyethylene-n-alkane solutions we have been able to predict the lower critical solution temperature and its dependence on the chain length of the alkane solvent, as well as the full coexistence curve and its variation with the polymer molecular weight.