Question 624876
let w = present age of the woman
let s = present age of the sister
:
"Four years ago a woman was three times as old as her sister."
w - 4 = 3(s-4)
w - 4 = 3s - 12
w = 3s - 12 + 4
w = 3s - 8
:
"in five years time she will be 20 years older than her sister."
She will always be 20 yrs older than her sister, that is a dumb statement!
Calculated to confuse you
Just say w = s + 20 
:
In the 1st equation replace w with (s+20)
s + 20 = 3s - 8
s = 3s - 8 - 20
28 = 3s - s
28 = 2s
s = 28/2
s = 14 yrs is the sisters age
then
14 + 20 = 34 yrs is the woman's age
:
:
Check our solutions in the statement:
"Four years ago a woman was three times as old as her sister."
34 - 4 = 3(14-4); confirms our solution