We describe a relatively simple, reliable, and fast approach for quantitative surface analyses by x-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) that significantly improves the accuracy of analyses of polycrystalline solids, The common formalism of XPS and AES is based on the assumption, now known to be incorrect, that elastic-electron-scattering effects are negligible. These effects can be taken into account by the use of correction parameters (two for XPS and one for AES) in a modified formalism. These correction parameters can be conveniently expressed in terms of the ratio zeta of the transport mean free path to the inelastic mean free path for a particular material and electron energy, and we give an improved procedure for determining this ratio for elemental solids and compounds at electron energies ranging from 50 to 2000 eV. We test the utility and validity of the derived correction parameters for XPS based on comparisons with parameter values and photoelectron intensities derived from Monte Carlo simulations for some 400 photoelectron lines in 27 elements excited by ME and Al characteristic x rays. It is pointed out that the systematic errors associated with the neglect of elastic-electron scattering in XPS depend on the instrumental configuration, and range from -20% to 30% for two WS configurations investigated here. With the use of the modified XPS formalism and the two correction parameters, these errors were reduced to between -3% and 2% for most of the photoelectron lines, although with a few lines the errors were as large as -10%. Good performance of the modified formalism for AES has been reported previously. We describe and discuss the application of this approach for surface analyses of multi-component solids. The improved procedure for calculating the ratio zeta can also be used for estimation of the mean escape depth of photoelectrons and Auger electrons.