In recent experiments, a sequence of changes in the wetting state ("wetting transitions'') has been observed upon increasing the temperature in systems consisting of pentane on pure water and of hexane on brine. In this sequential-wetting scenario, there occurs a first-order transition from a partial-wetting state, in which only a microscopically thin film of adsorbate is present on the substrate, to a "frustrated complete wetting state'' characterized by a mesoscopically, but not yet macroscopically thick wetting film. At higher temperatures, one observes a continuous divergence of the film thickness and finally, at the critical-wetting temperature, the complete-wetting state, featuring a macroscopic film thickness, is reached. This sequence of two transitions is brought about by an interplay of short-range and long-range interactions between substrate and adsorbate. The critical wetting transition is controlled by the long-range forces and is, thus, found by determining where the Hamaker constant, as calculated from a Dzyaloshinskii-Lifshitz-Pitaevskii-type theory, changes sign. The first-order transition involves both short-range and long-range forces and is, therefore, more difficult to locate. While the pentane-water system is well understood in this respect by now, a detailed theoretical description of the hexane-brine system is hampered by the a priori unknown modification of the interactions between substrate and adsorbate upon the addition of salt. In this work, we argue that the short-range interaction (contact energy) between hexane and pure water remains unchanged due to the formation of a depletion layer (a thin "layer'' of pure water which is completely devoid of ions) at the surface of the electrolyte and that the presence of the salt manifests itself only in a modification of the long-range interaction between substrate and adsorbate. In a five-layer calculation considering brine, water, the first layer of adsorbed hexane molecules, liquid hexane, and vapor, we determine the new long-range interaction of brine with the adsorbate across the water layer. According to the recent theory of the excess surface tension of an electrolyte by Levin and Flores-Mena, this water layer is of constant, i.e., salt-concentration independent, thickness delta, with delta being the hydrodynamic radius of the ions in water. Once this radius has been determined, the first-order transition temperatures can be calculated from the dielectric properties of the five media. Our results for these temperatures are in good agreement with the experimental ones. (C) 2003 American Institute of Physics.