Let numbers of eggs be m where m is between 10 and 20.
1st equation: 4x+3 = m
So the number of eggs could be (x=3,15),(x=4,19)
2nd equation 3y + 1 =m
So the number of eggs could be (y=4,13),(y=5,16) or (y=6,19)
Therefore, the number of eggs she had is 19