jenner,
Welcome to the pool forum! Though it is technically true that to determine what is called "carbonate alkalinity", you need to subtract 1/3rd of the CYA amount (when the pH is near 7.5) from the TA number, please don't worry about that kind of detail at this point. With calcium carbonate water balance you only need to be in the ballpark while it is your chlorine level, pH and CYA that are much, much more critical.
And yes, you are absolutely correct that adding acid will lower your pH as well as your TA. The correct procedure for lowering TA also involves aeration while holding the pH low (by adding acid) and is described in Ben's Lowering Your Alkalinity procedure, but I would not worry about your TA right now.
With your numbers, the primary problem is the high CYA and it could be higher than 100 depending on how it was measured (if measured visually, then the tube that does such measurements doesn't show marks higher than 100).
Though I will suggest some things you can do, I believe the first thing to do is to get yourself a good test kit if you have not already. If the numbers you reported were from a pool store, then I wouldn't necessarily trust them -- especially the CYA number. You can get a K-2006 test kit from Taylor Technologies rather quickly though more expensively, or you can wait and get a more economical PS-234 kit from Ben at PoolSolutions.
If you did the tests yourself, then getting your CYA down is the main priority. You could just follow Ben's Best Guess CYA chart and keep your FC level above 8 ppm and leave your CYA as it is for now, but you will probably be using a lot of chlorine this way since you can lose up to half in sunlight each day even with high CYA (though this time of year it's probably a lower loss rate). Since it is near the end of the swimming season, you may lose some of your CYA over the winter anyway so you might just want to wait and deal with the CYA issue upon opening in the spring when you "magically" may have less CYA in your pool (we're not certain of the exact reason, but many people have a large loss of CYA over the winter).
If you do want to lower your CYA, then the way to do that is to drain and refill a large portion of your pool with fresh water. You can use the "sheet" method by putting a large sheet over your pool and filling fresh water on top and draining from underneath or you can put in silage tubes and similarly fill the inside with fresh water. A less efficient method that uses more water to dilute is simply to drain from one end of the pool while filling with fresh water at the other. If you live in a place that gets a lot of rain in the winter, then you can use winter rains to fill and overflow your pool to dilute it (that's essentially what I do), but this doesn't work if you live in an area where the water freezes (since you need to lower your water level and shut down your pool, pump, etc. in this case).
When you dilute your CYA, you will automatically dilute (lower) your TA as well. That's another reason not to worry about your TA right now. You will also dilute everything else including your calcium and will need to restore that as well (that's another number that needs to be tested called Calcium Hardness or CH).
You should read about The BBB Method and use liquid chlorine as your primary source of chlorine (unless you have a Salt Water Chlorine Generator - SWCG). I suspect you got to your high CYA levels because of using Tri-Chlor tablets, is that right? If so, stop using them and use liquid chlorine (chlorinating liquid or unscented bleach). If you have an SWCG system, then the manufacturers recommend high CYA levels of around 70-80, but this does not sound like your situation.
By the way, do you have a plaster/gunite pool or a vinyl pool? This makes a difference with regard to whether water balance is important.
If you have any questions or need further clarification, please let us know.
Richard
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