Let Mark's age be M. Let the age of his son be B (boy) now. 3 years ago his son was B-3 years old, and in 3 years' time Mark will be M+3 years old, so M+3=9(B-3); M+3=9B-27, M=9B-30.
Let the youngest girl's age be Y, so B=4Y.
If we put the children's ages in order we have a number of possibilities:
- Y G G G 4Y
- Y G G 4Y G
- Y G 4Y G G
- Y 4Y G G G
One of the G's (girls) is 7Y and therefore older than B=4Y. So the boy can't be the eldest. So we eliminate (1).
What about (2)? The ages are 3 years apart so if the eldest G=7Y then 7Y-4Y=3 and 3Y=3 making Y=1, the age of the youngest girl. That makes the ages 1 4 7 10 14 which actually fits (4). So the boy is 4, the youngest is 1 and the middle girls is 7. M=9B-30=6 which cannot be! That seems to eliminate (2).
Now (3): 7Y-4Y=6, 3Y=6, Y=2: the ages are 2 5 8 11 14, the boy is 8 and the youngest is 2. M=9B-30=42.
That seems reasonable: Mark is 42, his son is 8 and his 4 daughters are 2, 5, 11 and 14.