100mL water can take salt some where from 35g (@0 C) to 40g (@100 C).
1 tablespoon table salt is roughly 18 grams, so 100ml water => 2 Tbs salt
A cup = 236ml, so the answer to your question is
Less than 5 Tbs, in teaspoon, it's 15.
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1 US cup = 236.588238 ml
So you can dissolve 84.9 g per cup
1 tablespoon of salt is about 20 grams
therefor four tablespoons or 1/4 cup of salt can be dissolved in one cup of water at room temperature.
It only increases solubility by about 10% if the water is boiling first.
96 tsp of salt
1 cup is 48 teaspoons
1 teaspoon is 0.02 cup
This answer is in US measure. Questions asked specifically on Imperial or metric measure shall be answered in kind.