Let's denote Jamie's age at present by J and Eden's age at present by E.
Since Jamie is three years younger, J is 3 less than E:
J = E - 3
Next year Eden will be one year older, that is, his age will be E + 1. She will also be twice as old as Jamie five years ago. Five years ago, Jamie's age was J - 5. So,
E + 1 = 2(J - 5).
Now we have a system of equations in two variables, J and E. We can substitute J from the first equation, J = E - 3, into the second equation:
E + 1 = 2(E - 3 - 5)
E + 1 = 2(E - 8)
Open the parenthesis on the right side:
E + 1 = 2E - 16
Subtract E and add 16 to both sides:
17 = E
So Eden's age at present is E = 17. Since Jamie is three years younger, her age at present is 17 - 3 = 14.
Next year, Eden will be 18, which is twice as old as Jamie five years ago, when she was 14 - 5 = 9. Both conditions of the problem are satisfied.
Let the present age of Eden = x
Therefore the present age of Jamie = x-3
( Since Jamie is 3 years younger than Eden)
After 1 year Eden’s age will be = x+1
Jamie’s age before five years was = x-3-5
So , x+1 = 2( x-8 ) as per the given condition
Hence the present age of Eden is 17 years and Jamie is (17-3) i.e. 14 years old.