Question

If you measure a tds of 1.4%, and you used a brew ratio of 15, what is the percent extraction?

Answer 1

Answer: the extraction is 18.2%.

Explanation:

Let's see few definitions:
TDS = Total Dissolved Solids = solids dissolved in the brew
PE = Percent Extraction = percent of solids extracted from the dry coffee grounds

The percent extraction can be calculated by the formula:
PE = TDS × Rm

where
Rm = ratio between the mass of the brew and the mass of dry grounds

Now, you need to consider the following facts:
1) every 1g of coffee absorbs 2g of water
2) the given brew ratio is 1:15, which means that for every 1g of grounds we use 15g of water

Let's call
x = grams of coffee grounds we want to use
Therefore the mass of the brew will be: 
m(brew) = water we use - water absorbed by the coffee
              = 15·x - 2·x
              = 13·x

Therefore,
Rm = m(brew) / x
       = 13·x / x
       = 13

Hence, the percent of extraction will be:
PE =  TDS × Rm
      = 1.4 × 13
      = 18.2