Three different sugar syrups (A, B, C) are to be combined, but only the total mass and overall concentration are specified. If the concentrations of A, B, and C are 5%, 10%, and 20% respectively, and the total mass is M, explain why you cannot uniquely determine all three masses from only the total mass and overall percentage, and give an expression showing one variable in terms of the other two.

Because the total mass equation x + y + z = M already determines each mass uniquely; therefore, z = M/x − y which gives a single solution

Because mixing three components always produces a unique solution regardless of equations, so the masses are uniquely determined and no expression is needed

Because there are only two independent equations for three unknowns, one variable must be expressed in terms of the other two; for example z = M − x − y, and the concentration equation becomes 0.05x + 0.10y + 0.20(M − x − y) = pM

Because concentrations cannot be used in linear equations for three components; you must convert to logarithms, which then determine unique masses