The article discusses the use of stable isotopes as tracers in environmental studies to determine the proportional contributions of multiple sources to a mixture. While the proportional contributions of \( n+1 \) different sources can generally be uniquely determined using \( n \) different isotope system tracers (e.g., \(\delta^{13}\)C, \(\delta^{15}\)N, \(\delta^{18}\)O) with linear mixing models, the number of potential sources often exceeds this limit, making it challenging to find a unique solution. The authors propose a method to determine bounds for the contributions of each source by examining all possible combinations of each source contribution (0–100%) in small increments (e.g., 1%). Combinations that closely match the observed mixture isotopic signatures within a small tolerance (e.g., ±0.1‰) are considered feasible solutions. The distribution of these feasible solutions is reported to avoid misrepresentation. The method has been applied to various environmental studies, including plant water use, geochemistry, air pollution, and dietary analysis. A computer program (IsoSource) is available to perform these calculations, and the article provides examples from published literature to illustrate its utility.The article discusses the use of stable isotopes as tracers in environmental studies to determine the proportional contributions of multiple sources to a mixture. While the proportional contributions of \( n+1 \) different sources can generally be uniquely determined using \( n \) different isotope system tracers (e.g., \(\delta^{13}\)C, \(\delta^{15}\)N, \(\delta^{18}\)O) with linear mixing models, the number of potential sources often exceeds this limit, making it challenging to find a unique solution. The authors propose a method to determine bounds for the contributions of each source by examining all possible combinations of each source contribution (0–100%) in small increments (e.g., 1%). Combinations that closely match the observed mixture isotopic signatures within a small tolerance (e.g., ±0.1‰) are considered feasible solutions. The distribution of these feasible solutions is reported to avoid misrepresentation. The method has been applied to various environmental studies, including plant water use, geochemistry, air pollution, and dietary analysis. A computer program (IsoSource) is available to perform these calculations, and the article provides examples from published literature to illustrate its utility.