Well, it's strange that the problem mixes gallons and kg, liters would be nicer. I'm guessing a mass fraction ratio for the problem (mass of salt:mass of water)?

55 gallons converts to 208 litres of water, which means 208 kg of water.

therefore: 208 kg * 34.5 * 10^-12 parts ~= 0.000000007176 kg of salt. (7.18 * 10^-9 kg)

then for the follow up you do the mass of salt divided by the new mass of water, 52 gallons -> 197 kg

7.18 * 10^-9 kg / 197kg = 3.64 *10^-11 -> 36.4 parts per trillion

hope this helps.