Control over the composition of III-V ternary nanowires grown by the vapor-liquid-solid (VLS) method is essential for bandgap engineering in such nanomaterials and for the fabrication of functional nanowire heterostructures for a variety of applications. From the fundamental viewpoint, III-V ternary nanowires based on group V intermix (InSb xAs 1-x, InP xAs 1-x, GaP xAs 1-x and many others) present the most difficult case, because the concentrations of highly volatile group V atoms in a catalyst droplet are beyond the detection limit of any characterization technique and therefore principally unknown. Here, we present a model for the vapor-solid distribution of such nanowires, which fully circumvents the uncertainties that remained in the theory so far, and we link the nanowire composition to the well-controlled parameters of vapor. The unknown concentrations of group V atoms in the droplet do not enter the distribution, despite the fact that a growing solid is surrounded by the liquid phase. The model fits satisfactorily the available data on the vapor-solid distributions of VLS InSb xAs 1-x, InP xAs 1-x and GaP xAs 1-x nanowires grown using different catalysts. Even more importantly, it provides a basis for the compositional control of III-V ternary nanowires based on group V intermix, and it can be extended over other material systems where two highly volatile elements enter a ternary solid alloy through a liquid phase.