Imagine I produce a concentrated Cold-Brew, with a 1:4 ratio.
How can I make a cup of diluted cold-brew that contains the standard ratio (1:15) ?
For the response consider explaining the math with:
PS: I don't think that is as simple as adding the n remaining parts, that's the reason why I'm asking this.
The math is fairly simple. You know for how much concentrated cold brew you will be using that it is at a ratio of 1:4. Since the resulting concentration of the cold brew is constant (since it has already been brewed) we only really care about the parts of water that are in it; 4 parts.
Therefore to calculate how much water you need to add to dilute your 1:4 concentrate into a 1:15 cup, divide the amount of concentrate you are using by 4 and then multiply that by the remaining parts you wish to add, which is 15 - 4 = 11 which gives you the amount of water you need to add in whatever units you measured the amount of concentrate you started with.
Using your example numbers:
Start with 100g of cold brew concentrate at 1:4 ratio. Each part of water is therefore 100/4 = 25g. The amount of water you will need to add is therefore 11 x 25g = 275g to result in a total amount of 375g in your final cup.
Check the final answer by doing a reverse calculation. If the concentrate is 1:4 and you have 100g of it, it means you started with 25g of ground coffee. Therefore making a 1:15 ratio cup of coffee with 25g of coffee means 25g x 15 = 375g of water must be added.
The answers align.
In general:
For an amount of cold brew to be diluted, c units, which has a coffee-to-water ratio of 1:n, the amount of each part of water in the cold brew, w equals c/n. The amount of water to be added to achieve a final ratio of 1:m is therefore w x (m-n) units.
Units are any form of measure of the liquid mass being used, in g, mL or others.
Using the dilution equation (assuming (incorrectly) that the moles concentration, correspond to the ratio of coffee:water of brewed product), the problem states:
C1 = cold-brew initial ratio
C2 = cold-brew final ratio
V1 = volume of initial cold-brew to consider
V2 = desired final volume
The dilution equation states:
C1*V1 = C2*V2
Replacing:
(1/4)*100 = (1/15)*V2
V2 = (100*15)/4
V2 = 375 grs
But, to achieve this 375grs final, we must dilute the original solution,
V2 - V1 = 375 - 100 = 275 grs of water.
Same result as Shiri.
