Calcium sulfate is a sparingly soluble salt, whose dissolution we could represent as :
#CaSO_4(s) rightleftharpoons Ca^(2+) + SO_4^(2-)#
This solubility will be governed by some equilibrium constant:
#K_(sp)# #=# #[Ca^(2+)][SO_4^(2-)]#.
If you want, you can search out for this #"solubility product"# on the web, but we don't need it here. Now, #K_(sp)# is a constant, and quoted for a given temperature (usually #298# #K#, because a hot solution can normally hold more solute than a cold one!). If the concentration of sulfate or calcium ion is ALREADY HIGH because of the presence of other sources of common ions, its solubility will be reduced with respect to the pure solvent. In the question, the aluminum sulfate was present in significant concentration - there were #3xx# as many sulfate ions.
Such a process is called #"salting out"#. If I had aqueous solutions of gold or platinum or rhodium salts, I would want to make sure that a maximal quantity of precious metal salt precipitated out from solution for collection, so I would try to salt it out.
