On a recent trip to a local orchard, the Nomial family picked four different kinds of apples - Braeburn, Cortland,...

On a recent trip to a local orchard, the Nomial family picked four different kinds of apples - Braeburn, Cortland, Fuji, and Rome. When they were done, they discovered that they had picked
• a total of 360 apples,
• twice as many Braeburn as Fuji,
• twice as many Cortland as Rome,
• 50% more Fuji than Rome.
How many of each kind of apple did they pick?