SOLUTION: A wool tapestry is 32 years older than a linen tapestry. Twenty years ago, the wool tapestry was twice as old as the linen tapestry. Find the present age of each. (I tried drawi

Let W be the wool tapestry age.

Let L be that of the linen tapestry.



Then your first equation is  

W = L + 32          (1)    ("A wool tapestry is 32 years older than a linen tapestry")



Twenty years ago the wool was  (W-20) years,  while linen was (L-20) years.

So, your second equation is 

W-20 = 2*(L-20)     (2)    ("Twenty years ago, the wool tapestry was twice as old as the linen tapestry")



Thus you have this system of two equations

W = L + 32          (1)
W-20 = 2*(L-20)     (2)



If you do understand it, then you understand the key moment in the solution.

The rest is just technique.



From equation (1), substitute this expression  W = L + 32  into the second equation.  You will get

(L+32) - 20 = 2*(L-20).


Now simplify it step by step:

L + 32 - 20  = 2L - 40

L + 12 = 2L - 40

12 + 40 = 2L - L

52 = L.


Answer.  The linen tapestry is 52 years old.  The wood tapestry is 32 years older, 52 + 32 = 84 years.