How does recrystallization work to purify if compounds have equal solubilities, but one is present in a greater quantity?

Every article or text I've read on crystallization states that it works by taking advantage primarily of differences in solubilities, but I've also been told that it can purify compounds with equivalent solubilities if one is present in a greater quantity. 


For instance, if there is a solution of 90% Compound A, and 10% Compound B, both with equal solubilities, a crystallization would supposedly purify it. But how? I've been told that, if say, 20% of the product was left behind in the solution, then it would consist of equal ratio of Compound A and Compound B, causing the formed crystals to be almost pure Compound A (saying a 1:1 ratio of A:B gets left behind). I was told that this ratio that gets left behind in the solution depends on the relative solubilities of the compounds, and not the quantity that which they were present. 


Is this accurate? How does this work exactly? I've read dozens of articles on crystallization and none of them seem to explain this sort of instance well, yet it seems very widely used in preparative chemistry.




Such recrystallization procedures are often used in organic chemistry where A and B would both be dissolved in hot solvent, but a large amount of A would precipitate as the solution cools. The rub here is that as A precipitates it will also adsorb some of the B. So to purify A further, often a second, or third, crystallization may be necessary. 


So imagine that 20 g of each of A and B are soluble in some quantity of the cold liquid. You start out with 100 g total of solute, so 90 grams of A and 10 grams of B dissolve in the hot solution. So all of the B would be soluble in the given quantity of cold solution, but only 20 grams of A. So 70 grams of A should precipitate. 


Notice that in order for this method to work all of A and B must dissolve in the hot solution. The idea is that crystals of compound A prefer to have A in the crystals rather than B. But if A has been coating grains of B, then if the whole solid particle is not dissolved, a lot of B will still be in the solid matter which didn't dissolve. 


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