A perturbed hard-sphere-chain (PHSC) equation of state is developed for normal fluids and polymers, including mixtures. The new PHSC equation of state for pure fluids uses a perturbation term based on the analytic solution by Chang and Sandler to the second-order perturbation theory of Barker and Henderson for the square-well fluid of variable width. The reference equation of state is the modified Chiew equation of state for athermal mixtures of hard-sphere chains as used in the original PHSC equation of state. The analytic solution by Chang and Sandler is simplified such that theory is readily extended to mixtures by conventional mixing rules. Using an optimum system-independent reduced well width, the new PHSC equation of state correlates the vapor pressures and liquid densities of saturated liquids with good accuracy. Combined with one-fluid type mixing rules for the perturbation term, theory is applied to liquid-liquid and vapor-liquid equilibria for binary mixtures where all components have the same reduced well width. Calculations were also made for a polymer solution where each component has a different reduced well width. In solvent/polymer systems, calculated liquid-liquid equilibria are sensitive to the reduced well width. The perturbation term, however, neglects chain connectivity.