Let's define the two liquids as Liquid 1 and Liquid 2.

• In Container A, the ratio of Liquid 1 to Liquid 2 is 5:1, meaning for every 6 parts of the mixture in A, 5 parts are Liquid 1 and 1 part is Liquid 2.
• In Container B, the ratio of Liquid 1 to Liquid 2 is 1:3, meaning for every 4 parts of the mixture in B, 1 part is Liquid 1 and 3 parts are Liquid 2.
• We want to mix the contents of Containers A and B in a certain ratio such that the final mixture has a ratio of 1:12 (Liquid 1: Liquid 2).

Let’s proceed step by step.

Let:

• $x$ be the amount of mixture taken from Container A.
• $y$ be the amount of mixture taken from Container B.

In Container A:

• The fraction of Liquid 1 is $\frac{5}{6}$.
• The fraction of Liquid 2 is $\frac{1}{6}$.

In Container B:

• The fraction of Liquid 1 is $\frac{1}{4}$.
• The fraction of Liquid 2 is $\frac{3}{4}$.

In the final mixture, the fraction of Liquid 1 should be $\frac{1}{13}$ (since 1:12 means for every 13 parts, 1 part is Liquid 1 and 12 parts are Liquid 2), and the fraction of Liquid 2 should be $\frac{12}{13}$.

Now, set up the equations:

For Liquid 1: $\frac{5}{6}x + \frac{1}{4}y = \frac{1}{13}(x + y)$

For Liquid 2: $\frac{1}{6}x + \frac{3}{4}y = \frac{12}{13}(x + y)$

You can solve this system of equations to find the ratio $x:y$.

Let's solve these equations step by step.The solution to the system of equations gives the ratio $x:y$ as approximately $-0.229y$. However, since ratios should be positive, this implies an issue with the values or setup in the equations.

Let me recheck and adjust the system to correct this.It appears I made an error in setting up the final system of equations. Let's reconsider the approach.

Since the goal is to find the correct ratio of the liquids, we'll aim for a positive solution. Would you like me to retry solving the problem, or clarify any steps so far?