2. Four years ago, the father was three times older than his daughters Elena and Natasha combined. Natasha was then twice as old as Elena. How old is Natasha, and how old is Elena if the father is now twice as old as both of them combined?
Solution. Let the father be $t$ years old, daughter Elena be $x$ years old, and daughter Natasha be $y$ years old. Four years ago, we have:

$$
t-4=3(x-4+y-4) \text { and } y-4=2(x-4) \text {. }
$$

From this,

$$
t=3 x+3 y-20 \quad y=2 x-4, \text { i.e. } t=9 x-32
$$

On the other hand, today we have

$$
t=2(x+y), \text { i.e. } t=6 x-8
$$

According to this,

$$
9 x-32=6 x-8
$$

from which we get $x=8$. Now $y=2 \cdot 8-4=12$. So Natasha is 12 years old, and Elena is 8 years old.