## Task 2 - 150722

The Winkler family has exactly three children.

On January 1, 1975, the oldest child was twice as old as the second, and this child in turn was twice as old as the youngest child. The mother was twice as old as her three children combined. The father was as old as the mother and the youngest child combined. The total age of all five family members was the same as that of the one grandfather, who was 64 years old when the oldest child was born.

How old was each of the mentioned individuals on January 1, 1975?

Note: All age specifications are to be understood in full years of life.
If on January 1, 1975, the youngest child is $x$ years old, then the second child is $2x$ years old, the oldest is $4x$ years old, the mother is $14x$ years old, the father is $15x$ years old, and the grandfather is $(64+4x)$ years old. According to the problem, we have

$$
x+2x+4x+14x+15x=4x+64
$$

from which it follows that $32x=64$, so $x=2$.

Thus, on January 1, 1975, the youngest child was 2 years old, the second child was 4 years old, the oldest was 8 years old, the mother was 28 years old, the father was 30 years old, and the grandfather was 72 years old.