Two boxes contained 155 lb of flour. if you take 20 lb from the first and add it to the second, the first box will contain 12/19 of what is now in the second. what amount of flour was originally in each box?

There were originally 80lb in the first box and 75lb in the second box.

The first equation describes the original weight in each box.
x+y=155
The second equation describes the weight after the 20 pounds is removed from the first box and added to the second:
, because 20 pounds is taken from the first box, x, and added to the second box, y; and that makes the first box equal to 12/19 of the second one.
We now have this system of equations:

We will simplify the bottom equation first by multiplying both sides by 19 to cancel the fraction:

We use the distributive property on the left, and cancel the 19 on the right:

We will move the 12y to the left side of the equation by subtracting:
19x-380-12y=12y+240-12y
19x-12y-380=240
Now we will cancel the 380 by adding:
19x-12y-380+380=240+380
19x-12y=620
Now our system looks like this:

To eliminate a variable, we want the coefficients to be the same.  We will multiply the top equation by 19 to achieve this:

Now we will subtract the bottom equation to cancel x:

Divide both sides by 31:
31y/31=2325/31
y=75

Substituting this back into our original first equation:
x+75=155
Subtract both sides by 75:
x+75-75=155-75
x=80