The combined age of Jack and John is 49. Jack is twice as old, as John was when Jack was as old as John is now. How old are the brothers?
Answer
Jack is 28, John is 21.
Let a and b be Jack’s and John’s age respectively.
So, a + b = 49
The difference in their ages (a – b), always remain the same.
“when Jack was as old as John is now” means Jack’s age was b and John’s age had to be:
b – (a – b) = 2b -a
Jack is now twice the age, so:
a = 2(2b – a)
a = 4b – 2a
3a = 4b
Substituting (a + b = 49), we can get b = 21 and a = 28.