If x is the youngest age then x+1, x+2, etc are the ages of the older children.
The youngest three are x, x+1, x+2. Add them together: 3x+3=42; x+1=14 so x=13. The children's ages go from 13 to x+6=19. (13+14+15=42.) The three oldest are 17, 18, 19 sum=54, and these were the first three to be born.
1997 1998 1999 2000 2001 2002 2003 (birth year)
19......18.....17.....16....15.....14.....13 (children's ages in 2016)
......(first born)...................(youngest)