So Seth is x years old and Mary is x+9.

In 1 year she will be x+9 + 1, and he will be x + 1,

So x+9 + 1 equals 3 times x + 1

x+9+1 = 3(x+1)

 x+10 = 3x+3
  -2x = -7
    x = 

So Seth is   and Mary is 9 years older or .

Checking:

In one year she will be  and Seth will be 

So we need to check to ss if  is three times 

 = 

So it checks.  That's a surprise because usually age problems 
have answers which are a whole number of years.  But not in this case.

Edwin