The sum of the ages of Dorothy and Dorileen is 41. In 5 years,
Dorothy will be twice as old as Dorileen. Find their ages 3 
years ago.

I'll give you the answer first. Then let's check it in the
problem.  That will help you learn how to set up word
problems, because you set them up the same way you check 
them.  

The correct answer is:  Three years ago, Dorothy was 26 and
Dorileen was 9. 


So Dorothy's age now = 29
and Dorileen's age now = 12 

>>...The sum of the ages of Dorothy and Dorileen is 41...<<

That says 

29 + 12 = 41  (which is correct)

>>...In 5 years, Dorothy will be...<<

She's 29 now, so in five years she'll be 29+5 or 34  

>>...twice as old as Dorileen...<<

Dorileen is 12 now, so in five years she'll be 12+5 or 17

and since

>>...In 5 years, Dorothy will be twice as old as Dorileen...<<

So 29+5 (which is 34) equals twice 12+5 (which is 17)

That is correct so the problem is correct.

----

Now here is how to solve it.  You'll see that the way to
set up a word problem when you DON'T know the answer is
VERY SIMILAR to the way to CHECK a word problem when you
DO know the answer.

Since their names start with the same FIRST letter "D", 
I will identify their ages by the LAST letter in their 
names instead of the first letter.
That is:

Dorothy's age now = y
Dorileen's age now = n 

>>...The sum of the ages of Dorothy and Dorileen is 41...<<

That says 

y + n = 41

>>...In 5 years, Dorothy will be...<<

Dorothy is y now, so in five years she'll be y+5

>>...twice as old as Dorileen...<<

Dorileen is n now, so in five years she'll be n+5

and since

>>...In 5 years, Dorothy will be twice as old as Dorileen...<<

So y+5 equals twice n+5
 Or y+5 equals 2(n+5)
 or
     y + 5 = 2(n + 5)

So we have this system of equations to solve:

   y + n = 41
   y + 5 = 2(n + 5)

Solve that system of equations and get

y = 29, n = 12

So three years ago Dorothy was 26 and Dorileen was 9.

Edwin