Determine the formula for the crystalline hydrate of metal sulfate if it is known that the mass fraction of salt in it is 51.351%

Determine the formula for the crystalline hydrate of metal sulfate if it is known that the mass fraction of salt in it is 51.351% and the mass of water in 1 mol of crystalline hydrate is 18 g less than the mass of anhydrous salt.

Let us denote the formula of the crystal hydrate as Mex (SO4) y ∙ zH2O, then we can compose a system of equations:
0.51351 = (xA (Me) + 96y) / (xA (Me) + 96y + 18z)
xA (Me) + 96y = 18z + 18
simplify and get
z = 18
xA (Me) + 96y = 342
Choosing the values of x and y, we find Ме = Al
Formula of crystalline hydrate Al2 (SO4) 3 ∙ 18H2O

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