Question

Abigail is 8 years older than Cynthia.Twenty years ago Abigail was three times as old as Cynthia.How old is each now?

Answer 1

A=c+8
a-20=3(c-20)
c+8-20=3c-60
8+60-20=3c-c
2c=48

c=24 years
a=32 years

Answer 2

Let 
C=Cynthia's age today
A=Abigail's age today

then
at all times
A=C+8......................(1)
twenty years ago,
A-20=3(C-20)
simplifying
A=3C-40...................(2)

Equate (1) and (2),
C+8=3C-40
8+40=3C-C
C=24
=> 
A=32

Check:  A-C=8... ok   A-20=12  C-20=4  => (A-20)=3(C-20) ...ok

Answer:
Abigail is 32, Cynthia is 24.