There is only one good way to learn to set up the equations
for word problems. That way is to practice by "cheating then
checking"!  That is:

1. Look up the answer in the back of the book.

2. Check that answer in the words to see WHY it is correct. 
Especially notice 'what equals to what'

3. Go through the SAME EXACT reasoning process, but using
unknowns instead, and when you get to any place where you
noticed that something was equal in the checking process,
make an equation.  You simply "check" the problem using
unknowns.

So you'll understand how to set up the problem. I'm going to
first tell you their ages in advance.  Then we'll check them
in the words.  Then I'll show you how to work the problem
doing the same thing, that is, "checking" with unknowns
instead of with knowns.

The girl is 6.
Her brother is 18.
Her sister is 14.

A girl is one-third as old as her brother

 [and so the girl's age of 6 equals 1/3 of 18, which checks!] 

   6 = 1/3(18)

and 8 years younger than her sister 

[and so the girl's age of 6 equals her sister's age
of 14 minus 8, which checks!].

    6 = 14 - 8 

The sum of their ages is 38 years. 

[so 6+18+14 does equal to 38. That checks!]
    
   6 + 18 + 14 = 38

----------------------------------------------

The girl is G.
Her brother is B.
Her sister is S.


A girl is one-third as old as her brother

[and so the girl's age of G equals 1/3 of B, 
which MUST check!] 

          G = 1/3(B)

and 8 years younger than her sister 

[and so the girl's age of G equals her sister's age
of S minus 8, which MUST check!].

          G = S - 8 

The sum of their ages is 38 years.

[so G+B+S does equal to 38. That MUST check!]
    
  G + B + S = 38

So we have three equations which we can combine into 
one:

      G = 1/3(B)
      G = S - 8
  G + B + S = 38

Solve the first equation for B and get 3G = B

Solve the second equation for S and get G + 8 = S 
   
Substitute 3G for B and G + 8 for S in the third
equation

    G + B + S = 38
 G + 3G + G+8 = 38

Now solve that for G, and we get

       5G + 8 = 38
           5G = 30
            G = 6 

Then although they didn't happen to be 
asked for, although they COULD have been,
we can get the brother's age from 
   
           3G = B
         3(6) = B
           18 = B

and the sister's age from

        G + 8 = S
        6 + 8 = S
           14 = S

  ------------------------ 

I'm sorry, but there is something wrong with this 
problem, because the answers come out that there 
are -4 children, the sum of the parents' ages
is -180 and the sum of the children's ages is -90. 
That does check mathematically, but nobody is a 
negative number of years old and no parents have a 
negative number of children.  Please correct the 
problem and re-submit it.

Edwin