Phase separation of biomolecules give rise to membraneless organelles that contribute to the spatiotemporal organisation of the cell. In most cases, such biomolecular condensates contain multiple components, but the manner in which interactions between components control the stability of condensates remained challenging to elucidate. Here, we develop an approach to determine tie-line gradients in ternary liquid-liquid phase separation (LLPS) systems, based on measurements of the dilute phase concentration of only one component. We show that the sign of the tie-line gradient is related to the cross-interaction energy between the polymers in the system and discriminates between competitive and cooperative phase separation. Using this approach, we studied the interaction between protein Fused in Sarcoma (FUS) and polyethylene glycol (PEG) polymer chains, and measured positive tie-line gradients. Our results show that PEG drives LLPS through an associative interaction with FUS and is not an inert crowder. We further studied the interaction between PolyA RNA (3.0±0.5kDa) and the protein G3BP1, and using the tie-line gradient as a reporter for the stoichiometry of polymers in the condensate we determined a G3BP1-to-PolyA RNA molar ratio of 1:4 in the dense phase. Our framework for measuring tie-line gradients opens up a route for the characterisation of interaction types and compositions in ternary LLPS systems.