Can this whiskey be a result of combining whiskey A, B, and C in any ratio? There is a whiskey made up of 64% corn, 32% rye, and 4% barley that was made by blending other whiskies together. I am trying to figure out if there is a chance the ratio of this whiskey could be the result of blending two, maybe three whiskies of different ratios. The possible whiskies: Whiskey A is 60% corn, 36% rye and 4% barley. Whiskey B is 81% corn, 15% rye, and 4% barley. Whiskey C is 75% corn, 21% rye, and 4% barley I have a feeling there is a possibility because these whiskies all have 4% barley, but I can't figure out if the other percentages match up in any 1:2:3 ratio in the blend. Any help will be greatly appreciated. Thank you.

Yes, and in infinitely many different ways!

Row reduce $\begin{bmatrix} 60&81&75&64\\\ 36&15&21&32\\\ 4&4&4&4\\\ \end{bmatrix}$ to get $\begin{bmatrix} 1&0&\frac{2}{7}&\frac{17}{21}\\\ 0&1&\frac{5}{7}&\frac{4}{21}\\\ 0&0&0&0\\\ \end{bmatrix}$.

Let's say:

$A$=ratio of Whiskey A in mixture

$B$=ratio of Whiskey B in mixture

$C$=ratio of Whiskey C in mixture

From the row reduction we get the relations: $$(*)A=\frac{17}{21}-\frac{2}{7}C, B=\frac{4}{21}-\frac{5}{7}C$$

Since $A,B,C$ are all between $0$ and $1$, these relations put a restriction on $C$: namely $C\leq\frac{4}{15}$. So choose your favorite value for $C$ in the appropriate range, plug it into the equations in $(*)$. That will give you the amounts of whiskeys A and B you need to get the desired mixture.