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

                                                = x-8

So , x+1 = 2( x-8 ) as per the given condition

       x+1=2x-16

      2x-x=16+1

      X=17

Hence the present age of Eden is 17 years and Jamie is (17-3) i.e. 14 years old.

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.