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So I did the math on the size of my grow bed based on the basic rules of thumb and if I have a 22in long by 11in deep grow bed that equals to 1.68 or well just say 2sq.ft. which means I need about 2 pounds of fish in my tank. If I only have a 10 gallon tank what is the maximum amount of fish I can have and how many goldfish do I need to make up 2 pounds? Also what is a rough estament on how many plants I can grow? 

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Relax Dan, that rule of thumb is saying that with 1.68 cubic feet of grow bed you have filtration for up to 1.68 lb of fish.  So if your system could grow out a fish to 1 lb, I would say only stock it with one or two of some type of fish that would grow that big.

Since your system is tiny and your 10 gallon fish tank can't really support two pounds of fish, don't worry about it.  Just get some aquarium fish to start.  I don't really recommend the cheapest feeder goldfish because they are often deformed or sick and sold to be food, not necessarily to survive for long.  Sometimes you get lucky with the cheapest fish though but the next step up in goldfish may be more likely to survive for you.  Or you might cycle up fishlessly and then add half a dozen goldfish later.  No worries goldfish are big poopers so they should feed your plants well enough.

Biggest trick is you need lots of light to grow plants well but you need to protect such a small system from extreme temperatures so it probably can't be outdoors.

How much plants you can grow will depend on what kind of plants you grow and how fast they are.  Lettuce and herbs are probably your best choice for an indoor system like this.  You can grow lots and lots of baby lettuce and keep re-planting as you harvest.

Ok that's a relief, thank you TC you have been a huge help!

So the only problem I have left right now is my plants are starting to show signs of multiple nutrients deficiency, how do I add things like calcium and, iron, magnesium and copper to the water without getting to much and killing the fish? And how do I monitor the levels of specific metals like that in the water?

I'd just get a little maxicrop and add a cap full every month or so which will take care of potassium and trace elements.  Chelated iron is usually only needed if your pH is high.  A pinch or small spoon full every few weeks only when the plants show signs of deficiency.  If your tap water is hard, you many not need to add calcium very much and if you do, you can use a little bit of calcium carbonate (shells or limestone chips) when the pH falls, add them in a mesh bag so you can take them out if the pH goes too high.

Otherwise for home systems, usually we don't get much more scientific than that.

Ok thanks, what is maxicrop?

Maxicrop is seaweed extract.  N-P-K numbers are 0.1-0-1.0

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