Hello, Cotton,
First, find the percentage of nitrogen's mass in NH3 by taking the total molecular mass (17g/mole) and dividing it into the mass due to nitrogen (14). That yields 0.824, or 82.4% of the mass of NH3 is due to the N atom. If one has 350.0 grams of NH3, then one has 350.0g * 0.824 grams of N. I get 288.2 grams N.
Bob