Here, the assumption is that prices will fall as the companies want to gain market share by cost competition.
Based on this assumption, the answer assumes that gross margin of 3.8% stays the same (which is a significant assumption).
With a gross margin of 3.8%, this means that 96.2% of the price goes to cost. Costs, as calculated, are now $2300. Therefore, this leads us to the conculsion that the new price will be $2390.85. To calculate this, $2,300 / 96.2% (which is the equation shown in your question).
Of course, the earlier assumptions on gross margin staying the same are worth questioning.