Jamie is three years younger than eden. Next year eden will be twice as old as Jamie five years ago? Find their present ages.
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.