Balance ba(no3)2 + na2so4 --> baso4 + nano3

Ba(NO₃)₂  +  Na₂SO₄  → BaSO₄ + NaNO₃

By Trial and error.

Ba(NO₃)₂  +  Na₂SO₄  → BaSO₄ + 2NaNO₃

Check:

             LHS            RHS
Ba           1                1
N             2                2
S             1                1
O      3*2 + 4 = 10         4 + 2*3 = 10

Polstyrene foam is more commonly known as styrofoam. When clumped together, styrofoam would float on water. So, the easiest and the most cost-efffective way of separating sand from styrofoam is flotation with the use of water.

Other processes are also available. Polystyrene is soluble in organic solvents like acetone, toluene or benzene. By adding these solvents, polystyrene would react so that you are left with only the sand. This process is called solvent extraction. If you want to recover the styrofoam, just evaporate the solvent out and you are left with a solid form of the polystyrene.