## Input Interpretation

The given chemical equation is:

* (NH4)3PO4 + 3 H2O → 3 NH3 + H3PO4*

The reactants are ammonium phosphate and water, which react to produce ammonia and metaphosphoric acid.

## Balanced Equation

To balance the chemical equation, we need to add stoichiometric coefficients, c, to the reactants and products. Let's represent these coefficients as follows:

* C1 (NH4)3PO4 + C2 3H2O → C3 NH3 + C4 H3PO3*

Next, we need to set the number of atoms in the reactants equal to the number of atoms in the products for nitrogen (N), hydrogen (H), phosphorus (P), and oxygen (O). This gives us the following system of equations:

*N: 3c1 = c3*

*H: 12c1 = 2c2 + 3c3 + c4*

*P: c1 = c4*

*O: 4c1 = c2 + 3c4*

Since the coefficients are relative quantities and underdetermined, we choose a coefficient to set arbitrarily. Typically, we set one of the coefficients to one to keep the coefficients small. For instance, let's set c1 = 1 and solve the system of equations for the remaining coefficients:

*c1 = 1*

*c2 = 1*

*c3 = 3*

*c4 = 1*

Substituting these coefficients into the chemical reaction gives us the balanced equation:

*(NH4)3PO4 + 3 H2O → 3 NH3 + H3PO4*

**Answer**

The balanced chemical equation is

* (NH4)3PO4 + 3 H2O → 3 NH3 + H3PO4. *

This equation represents the reaction between ammonium phosphate and water to produce ammonia and metaphosphoric acid.