In a recent paper, we determined the pair structure and free energy for a binary system of two weakly coupled replicae of a soft-sphere fluid, using fluid integral equations, to locate the Kauzmann temperature2 TK and the “random first order transition” (RFOT) temperature Tcr to an “ideal glass.” In this model, particles interact via the repulsive pair potential v(r)=ε(σ/r)12v(r)=εσ/r12 (where ε and σ are the energy scale and particle diameter); its excess (non-ideal) equilibrium properties depend on a single dimensionless parameter Γ = ρ*/(T*1/4) (where ρ* = Nσ3/V and T* = kBT/ε are the reduced number density and temperature). Atoms of opposite replicae (labeled 1 and 2) interact via an attractive potential, chosen to be v12(r)=−ε12[c2/(r2+c2)]6v12(r)=−ε12c2/(r2+c2)6, where ε12 sets the energy scale and c < σ is the range parameter chosen such that an atom of replica 1 interacts with at most one atom of replica. The pair structure of this symmetric binary system is characterized by two pair distribution functions (p.d.f.) g11(r) ≡ g22(r) and g12(r), related to two direct correlation functions by two coupled Ornstein-Zernike relations and a closure relation. For the latter, we chose the hyper-netted chain (HNC) closure and a thermodynamically self-consistent closure due to Rogers and Young (RY). The HNC approximation is thermodynamically inconsistent but allows the excess free energy Fex to be expressed in terms of pair correlation functions alone, while the more accurate RY closure requires a tedious thermodynamic integration of the excess internal energy to calculate Fex as a function of Γ