SOLUTION: if a family with only two daughters, one of the daughters is currently three times as old aa the other. two years ago the older daughter was four times as old as the younger sister

Let x be the current age of the younger daughter.

Then the age of the oldest is 3x, according to the condition.


Two years ago the younger was  x-2 years old, while the older was 3x-2 years old.


The problem says


    4*(x-2) = 3x - 2.


Simplify step by step and find x


    4x - 8 = 3x - 2

    4x - 3x = 8 - 2

     x      = 6.


ANSWER.  The younger daughter is 6 years old now.  The older is 3*6 = 18 years old.


CHECK.  2 years ago they were 4 years and 16 years old, with the ratio of 4.    ! Correct !