The lees have 3 children. the oldest is twice as old as the youngest. the middle is 5 years older than the youngest. if the sum of the age is 57, how old is each child?

Oldest = 2 times Youngest -> O = 2*Y
Middle = Youngest + 5 -> M = Y+5
All of them together is 57 -> O + M + Y = 57

So you have these three equations:
(1) O = 2*Y
(2) M = Y+5
(3) O + M + Y = 57

Now you want to reduce the number of variables. You can change the second equation to be Y = M-5 and then plug in "M-5" wherever there is currently a Y:

(4) O = 2*(M-5) = 2*M - 10
(5) O + M + (M-5) = 57 
    which becomes O + 2M = 62

Then you plug in the "O" equation (4) into (5) which gives you
(2M-10) + 2M = 62 which reduces to 4M = 72.

So now I know M is 18. 
I can now plug that into my other equations:
(4) O = 2*18 - 10 which means O = 26.
Now I plug that into (1) from the top:
26 = 2*Y which becomes 13 = Y

So now I have O, Y, and M
Oldest is 26
Middle is 18
Youngest is 13

Reading the sentence again, you can see that this makes sense.