The following equation $$0.27a+0.1b+0.13c=70$$ can admit many solution. Is there any software/methods I can use so that I can have a large list of all the possible numerical solutions to this equation?
The background to such a problem
So I am designing for my friend a recipe, and I know chicken, yoghurt and eggs, contain 0.27g, 0.1g and 0.13g of proteins per gram respectively. Suppose I would like to have 70g of proteins, what are the combinations of the respective amount of food to make up the desired amount of proteins? In principle I can just determine randomly the amount of chicken I'd like to have and that of eggs and solve for the remaining term, but is there anything I can do so that I can have a list of all possible positive solutions to choose from (to save the hassles?)?