As a heavily simplified example of my problem:
- Water weighs 1 gram per ML
- Alcohol weighs 0.5 gram per ML (not true of course, but humour me)
I have 100mls of water, so this has a weight of 100grams
I want to adjust the weight to 90grams by pouring out some water and substituting it with alcohol. I still want the final volume to be exactly 100mls.
I've wracked my brain on this, I feel like I need to go back to high school. Please show me the way.
This is a single variable problem: the volume $x$ of water to be replaced with alcohol. The question is, what is the mass of the resulting $100$ mLs of liquid?
The initial mass was $100$g.
You remove $x$ grams ($x$ mL) of water, the mass is now $100-x$.
You add $0.5x$ grams ($x$ mL) of alcohol, the mass is now $100-x+0.5x=100-0.5x$.
So you need to solve $100-0.5x=90$.