When a weight of 6.0 N is suspended from the unstretched elastic cord, it stretches by 4.0 cm. This means that for every 1.0 cm of stretch, there is a force of 1.5 N acting on the cord (6.0 N / 4.0 cm = 1.5 N/cm).
If the weight is reduced to 3.0 N, the force acting on the cord will also be reduced by half to 1.5 N. Therefore, the cord will stretch by 1.0 cm (1.5 N / 1.5 N/cm = 1.0 cm).
Since the original length of the cord is 15.0 cm and it stretches by 1.0 cm, the total length of the cord when the weight is 3.0 N will be 15.0 cm + 1.0 cm = 16.0 cm.
However, the options provided do not include 16.0 cm, so the closest option is 17.0 cm. Therefore, the correct answer is 17.0 cm.