Marie is one-ninth as old as her mother.  In three years,
she will be one-forth as old as her mother will be then.  
Find their present ages.  

Rewrite it without fractions:

Marie's mother is 9 times as old as Marie is..  In three years, her
mother will be 4 times as old as Marie will be then.  
Find their present ages. 


Let Marie's age be x
Then Marie's mother's age is 9x
Marie's age in 3 years will be x + 3
Marie's mother's age in 3 years will be 9x + 3
Marie's mother's age in 3 years will also be 4(x + 3)

Therefore

9x + 3 = 4(x + 3)

9x + 3 = 4x + 12

5x = 9 

x = 1.8 years and her mother is 16.2

That checks because:

Marie (who is 1.8 years old) is one-ninth as old as her mother, who is 16.2)

That checks because 1/9 of 16.2 is 1.8 

In three years, she will be 4.8, and mother will be 19.2  

That checks because 1/4 of 19.2  is 4.8.

So Marie is 1.8 years old and her mother is 16.2 years old.

I guess there have been mothers who had a baby when they were 
14.4 years old, but this is hopefully a rare occurrence.

Edwin