Let
A = present age of Albert
B = present age of Bryan

Present 
xyrs hence 
yyrs ago 
zyrs ago 
10yrs hence 
Albert 
A 
A + x 
A  y 
A  z 
A + 10 
Bryan 
B 
B + x 
B  y 
B  z 
B + 10 
Albert is as old as Bryan will be...
$A = B + x$
$x = A  B$
... when Albert is twice as old as Bryan was...
$A + x = 2(B  y)$
$A + (A  B) = 2(B  y)$
$2A  B = 2B  2y$
$2y = 3B  2A$
... when Albert's age was half the sum of their present ages
$A  y = \frac{1}{2}(A + B)$
$2A  2y = A + B$
$A  B = 2y$
$A  B = 3B  2A$
$3A = 4B$
$B = \frac{3}{4}A$
Bryan is as old as Albert was...
$B = A  z$
$z = A  B$
... when Bryan was half the age he will be ten years from now
$B  z = \frac{1}{2}(B + 10)$
$B  (A  B) = \frac{1}{2}(B + 10)$
$2B  A = \frac{1}{2}(B + 10)$
$4B  2A = B + 10$
$3B  2A = 10$
$3(\frac{3}{4}A)  2A = 10$
$\frac{1}{4}A = 10$
$A = 40 ~ \text{yrs old}$ ← present age of Albert (answer)
$B = \frac{3}{4}(40)$
$B = 30 ~ \text{yrs old}$ ← present age of Bryan (answer)
Question:
Question:
Why is the mathematical expression for ...when Albert is twice as old as Bryan was...
A + x = 2(B  y)
And not
A = 2(B  y) since "when Albert is" refers to the present?
"When Albert is" refers to
In reply to Question: by nmjanas
"When Albert is" refers to the time when "Albert is as old as Bryan will be" (the previous statement) which is x yrs in the future. Similar interpretation for "Bryan is as old as Albert was when Bryan was half the age he will be ten years from now"