含乘积项的四元四方程组求解及蒸馏组分计算技术问询

Hi everyone, I'm stuck working through a system of equations linked to a distillation composition problem and could use some guidance.

First up, here's the system of equations I've put together:

$$
\begin{align*}
0.3 A &= 0.1 B \
B C &= 0.37 (A + B) \
0.5 A + D B &= 0.43 (A + B) \
C + D &= 0.9 B
\end{align*}
$$

I’m aware I won’t get a numerical answer for any single variable here—what I actually need are the ratios between these variables.

Full Task Context & Clarifications #

To add clarity, here’s the full task I’m working on:

The pot contains 43% liquid 1, 20% liquid 2 and 37% liquid 3. If we move all of liquid 3 into a second pot, while leaving the first at a 50/50 blend of liquids 1 and 2, what is the exact composition of pot 2 if it has 10% liquid 2?

I started with the equation V0 = V1 + V2 (where V0 is the initial total volume, V1 and V2 are the volumes of pot 1 and pot 2 after distillation) and derived the rest of the equations from the given data. I can’t see another way to approach this, but I’m stuck solving the system as is—open to any suggestions or alternative methods!

One more critical detail I forgot to include earlier:

The transfer method is distillation with no losses. ALL of liquid 3 is moved to pot 2, while liquids 1 and 2 are split between the two pots such that pot 1 ends up with a perfect 50/50 blend of liquids 1 and 2. Also, pot 2 has 10% liquid 2.

备注：内容来源于stack exchange，提问作者Ivan