I know this is probably a very basic question but I see a lot of people reference that they maintain 100% hydration or other percentages. How is this determined?
where a starter is maintained at 100% hydration it simply means that for every 100g of flour in the starter, there is also 100g of water. So if a starter is maintained a 60% hydration, that means for every 100g of flour, you would have 60g water. The first is an example of a liquid starter, the second one is a stiff starter. Each brings its own characteristics to the resulting bread, as they behaver slightly differently during fermentation.
So, what will be hydration of:
50g "old starter"
I maintain 2 starters; the rye starter is maintained at 167% hydration, and the wheat levain is maintained at 60% hydration. So I know what the original hydration of the old starter is. In your example, the old starter should be 100% hydration, so there are 25g flour and 25g water in it. If a starter is maintained with inconsistent levels of hydration, then the water levels in the old starter might be unknown.
This is going to be close to 100% hydration, but not quite...although probably good enough to be 100% hydration for practical use.
Let's say that 50g of old starter is pretty wet, 170% hydration (fairly common if you feed at equal parts by volume); this means old starter is 18.5g flour + 31.5g water. This would mean your new starter is actually 118.5g flour + 131.5g water = 111% hydration for new starter.
On the opposite end, let's say your old starter is really dry (55% hydration, like bagel dough); that would mean old starter is 32.3g flour and 17.7g water. This would mean your new starter is actually 132.3g flour + 117.7g water = 89% hydration for new starter.
So you can see both are close already. You can also see that after one or two of the same feedings, you'll practically be at 100% hydration. You can speed the process of getting to 100% hydration by just using a smaller amount (25g or so) of old starter, and/or increasing the amount of fresh flour & water you are using to feed (e.g., use 200g of each instead of 100g).
100% hydration means equal weight flour to water, so if you feed it 200g flour, you add 200g water.
If you say you have a "60% hydration dough", then it would be 120g water to 200g flour. And so on.
More on baker's math here.
Hydration equals weight of water divided by weight of flour. 10 oz of water and 15 oz of flour equals 66% hydration (10 divided by 15). 12 oz water and 15 oz flour equals 80% hydration.