"Impossible" Chemistry Balancing Problem?

Question

Here is the exact text of the problem:

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Phosphorus occurs naturally in the form of fluorapatite, CaF2 * 3Ca3(PO4)2, the dot (asterisk) indicating 1 part CaF2 to 3 parts Ca3(PO4)2. This mineral is reacted with an aqueous solution of sulfuric acid in the preparation of a fertilizer. The products are phosphoric acid, hydrogen fluoride, and gypsum, CaSO4 * 2H2O. Write and balance the chemical equation describing this process.

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Let's see your best efforts!

Answer 1

The actual balanced equation is

CaF2*3Ca3(PO4)2 (s) + 10 H2SO4 (aq)  --->  6 H3PO4 (aq) + 2 HF (g) + 10 CaSO4 (s)

Because the Calcium sulfate is generated in an aqueous solution, the crystals formed will include water of hydration (two water molecules for every Calcium sulfate).  This is why Gypsum is listed as one of the products.  This is also why it is justified to add the water in the equation:

CaF2*3Ca3(PO4)2 (s) + 10 H2SO4 (aq) + 20 H20 (l)  --->  6 H3PO4 (aq) + 2 HF (g) + 10 CaSO4*2H2O (s)

Answer 2

Sure you can because this is happening in aqueous solution, right? The only time I would simplify acid and base reactions is only adding H+ to an acidic solution problem and only OH- to a basic solution problem.  

Answer 3

Adding water as a reactant helps to balance out the H's and O's

Here you go. Coefficients are, from left to right: 1, 10, 20, 6, 2, and 10

CaF2▪3Ca3(PO4)2 + 10 H2SO4 + 20 H2O ==> 6 H3PO4 + 2 HF + 10 CaSO4▪2H2O