A 50-year-old and his three sons are celebrating their birthdays today. Knowing that age of the father is equal to twice the sum of the ages of his sons, and to 13 times the difference in age between the youngest and the youngest, knowing also that the age of the eldest is equal to three times the difference in age between his brothers and that a quarter of the age of the eldest is equal to a third of the age of the youngest, determine the age of each person, on this birthday, after finding the solution set if:

x is the age of the father; y is the age of the eldest; z is the age of the youngest; w is the age of the youngest;