Have you heard of Bakers Math? I hadn't until I started reading my new book on Sourdough. It is a formula used by bakers who measure ingredients as a percent of the total amount of flour rather than relying on cups etc. Since they count the flour as 100%, the salt, liquid, and yeast are designated as a specific percent based on the ratio of the ingredient as compared to the flour.
One reason they use weight rather than cups is because each cup of flour does not always weigh the same. A cup of flour can weight between 115 and 155 g depending on how packed it is, the type of flour and if its been sifted. This explains why one time the recipe comes out beautifully while another time it might be too thick.
As a result of this inconsistency, bakers developed a formula which yields a more consistent product due to having a more precise recipe. Think about this, it's a real life application of percentages and ratios in a situation other than shopping and scale models.
The way it works is say you are starting with 500 grams of flour. The salt is 2% so that is 500 x .02 or 10 grams of salt. The liquid might be 70% or 500 x .70 or 350 grams of water while you need 1.2% yeast or 500 x .012 = 6 grams of yeast. I've seen recipes requiring anywhere from 60% to 80% for the liquid. If you add anything, it will be a percent of the flour. This requires 500 + 10 + 350 + 6 or a total of 866 grams of dough.
So how is this used? Its used in two different ways. First you are given the weight in pounds or grams and you want to know if the other ingredients fall within the accepted percentages. So if you have 100 pounds of flour, 60 pounds of water, 5 pounds of yeast and 2 pounds of salt. So you can easily figure out the percentages by division.
60/100 = .6 = 60%
5/100 = .05 = 5 %
2/100 = .02 = 2%
It looks like the yeast is a bit high so I'd consider reducing it.
You can also go the other way if you are given percentages and you need to find the weight of each ingredient. This is the math done in the example with the 500 grams of flour. So it is possible to use math to go either way.
This basic formula can be used to recalculate by knowing how many pounds or grams of dough your original recipe uses and the total percentages of all the ingredients for that recipe. To find your conversion factor you divide the desired new weight of the dough by the percent of the original recipe. Then multiply the percents by the conversion factor to give the new weights of each ingredient.
Lets look at this example. Your original recipe makes 150 lbs of dough but you want to readjust the recipe for 100 lbs. The percent of your ingredients adds up to 175.9% so you divide 100 by 175.9 which gives a conversion factor of .57 rounded. So you multiply each individual percent by the conversion factor assuming the flour is 100%.
Flour - 100% x .57 = 57 lbs
Water - 70% x .57 = 39.9 lbs
Salt - 2 x .57 = 1.14 lbs
Yeast 1.2 x .57 = .69 lbs
So this gives about 100 lbs.
If you want to see this type of math in more detail check out King Arthur's Flour website. It has great examples and I'm going to throw a couple of these in class for warm-up. Hope you find this interesting.