Am I anywhere close on this?
Yes and no. You do not need to consider the mass of 50ml of water, but you need to take in account of sulphate precipitated.
Let the formula of epsom salt be MgSO
4.xH
2O
The solvation process can described as:
MgSO
4.xH
2O -> Mg
2+ (aq) + SO
42- (aq) + x H
2O (l)
from this solution the student isolated 9.30g of anhydrous BaSO4 (s) which is formed in the following reaction.
From here, you can work the number of moles of sulphate and magnesiums ions present in 9.86g of epsom salt given you know the required stoichiometric ratio.
Next, you can deduce how much of 9.86g Epsom salt is water by using mass balance.
The unknown quantity x can be found as the molar ratio of water molecules to sulphate ions in 9.86g of Epsom salt.