SOLUTION: karen is twice as old as marie.four years from now,the sum of their ages will be 44.how old is karen?

Make this chart:

       age     age 
       now    then
KAREN      |  
-------------------
MARIE      |   
------------------

You can do it with either one unknown or two unknowns.

With one unknown:

We must define one of their ages in terms of the other.
Then the "other" will be the one we will represent by an 
unknown (letter).

Since the sentence

defines Karen's age in terms of Marie's age,

we choose Marie's age to be the unknown, M.

We will define Karen's age in terms of M, Marie's age,

Karen's age now = 2 times Marie's age M now, so

Karen's age now = 2M

We fill in the chart with M for Marie's age now and 2M
for Karen's age now
 
       age     age 
       now    then
KAREN  2M  |  
-------------------
MARIE   M  |  
-------------------

Then we read
 

So we add +4 to each of their ages to
get their ages then:

       age     age 
       now    then
KAREN  2M  |  2M+4
-------------------
MARIE   M  |   M+4
------------------

Then we read:

So we add (2M+4) plus (M+4) and set that equal to 44:

      (2M+4)+(M+4)=44
          2M+4+M+4=44
              3M+8=44
                -8 -8
              -------
              3M  =36
                 M=12

So Marie is 12.  Then Karen's age is 2M or 2(12) or 24.

Checking:  Four years fom now they will be 16 and 28, and those
have sum 44.  it checks.

=======================

With two unknowns:

       age     age 
       now    then
KAREN   K  |   K+4
-------------------
MARIE   M  |   M+4
------------------




Simplify and solve that system of equations 
and you'll get K=24 and M=12

Edwin