Combining two liquids with different weights to achieve a desired volume and weight

Question

I have two liquids - water and alcohol, each liquid has a different mass

• Water weighs 1 gram per ML
• Alcohol weighs 0.5 gram per ML (just for the sake of the example)

I wish to combine these liquids using a yet to be determined ratio to produce a volume of 2mls and a total mass of 1.75grams

I think my formula is this -

 1      0.5     1.75
---  +  ---  =  ---
 x       y       2

Is my formula correct? And is there a technique for solving this?

Answer 1

Let $x$ denote the amount of milliliters of water.

Let $y$ denote the amount of milliliters of alcohol.

Then you want:

• $x+y=2$
• $1x+0.5y=1.75$

This is a system of two equations with two variables, easy to solve:

• $x+y=2 \implies x=2-y$
• $1x+0.5y=1.75 \implies x=1.75-0.5y$
• $[x=2-y]\wedge[x=1.75-0.5y] \implies 2-y=1.75-0.5y$
• $2-y=1.75-0.5y \implies 0.5y=0.25 \implies y=0.5$
• $[x+y=2]\wedge[y=0.5] \implies x+0.5=2 \implies x=1.5$