The solution of the first-order Ornstein-Zernike equation is applied to improve the Percus-Yevick radial distribution function (RDF) of hard spheres, where the direct correlation function is postulated to hold the Yukawa form outside the hard core. Thermodynamic consistency is imposed to determine the parameters in the postulation. Very simple analytical expressions for the Laplace transform of the RDF are obtained for hard spheres and hard sphere mixtures. The resulting RDFs are compared satisfactorily with computer simulation data.