rohanbnj wrote:
Same here, could you elaborate a bit more on the thought process and the why? I lucked out on this question, but not sure why
I think
Hoozan did a great job getting to why the total quantity of the containers are equal and of opposing parts, but I think that intuition can to be expounded upon.
Let me try to explain the best I can.
Taking a look at the following containers:
1) Liquid \(A_{1}:B_{1}\) ==> 1:2. This means the total volume of the can is \(3x = 1x + 2x\)
2) Liquid \(A_{2}:B_{2}\) ==> 2:1. This means the total volume of the can is \(3y = 2y + 1y\)
The goal of this problem is to see what portion of each can needs to be mixed for A to Equal B.
i.e. Figure out \(3x:3y\)
We can set this equation up this way because we do not know the exact quantities of liquid respective to each container (e.g. x vs y), but we know that it is dispersed in parts within each container in a formulaic way (e.g. 1:2).
Now we are trying to combine the mixtures to have equal parts of A to B.
This means we can set up a system of equations where \(A_{1} + A_{2} = B_{1} + B_{2} \) (same as saying 1:1).
\(x + 2y = 2x + y\) which just gives us \(y = x\).
This means that the total volume of each can (\(3x\) and \(3y\)) must be equal to each other
IF we set the total parts of A equal to the total parts of B.
\(3x:3y\) is \(1:1\).