Let a, b, c, d be constants such that
a Na₃P + b CaF₂ → c NaF + d Ca₃P₂
Count the atoms on either side.
Left:
Na = 3a, P = a, Ca = b, F = 2b
Right:
Na = c, F = c, Ca = 3d, P = 2d
To get the same number of atoms of each element on both sides, we would have
3a = c
a = 2d
b = 3d
2b = c
If we let d = 1, we get a = 2, b = 3, and c = 6, so the balanced equation is
2 Na₃P + 3 CaF₂ → 6 NaF + Ca₃P₂
