Cloud-point and spinodal curves of the system methylcyclohexane (MCH)/polystyrene (PS) are calculated with the aid of the Sako-Wu-Prausnitz equation of state (SNAT-EOS). To describe the molecular-weight polydispersity of the polymer influencing the phase equilibrium and the stability, continuous thermodynamics is applied. The system MCH/PS is particularly interesting. In a certain temperature region its pressure-concentration diagram shows both a curve with a lower critical point (LCP) and a curve with an upper critical point (UCP). Lowering the temperature both curves become closer and merge, finally, forming a hour-glass shaped two-phase region. For several years this behaviour has been well known from experimental data concerning a nearly monodisperse PS sample. Firstly, we prove the SWP-EOS to be able to describe these data. Secondly, by computer simulations we investigate the transition of the UCP/LCP curves into the hour-glass shaped curves for the polydisperse case never studied before. This transition is demonstrated to be quite different from that of solutions of monodisperse PS samples in MCH. Thirdly, we apply the SWP-EOS to a real system consisting of MCH and a PS sample with a broad molecular weight distribution and, compare the results with the experimental findings.