John is now twice as old as he was when Mary was three years older than he is now,

but he is only half as old as Mary is at present. Now, how old are they? 

:

Let j = J's present age

Let m = M's present age

Let d = m-j; the difference in their ages

:

"he is only half as old as Mary is at present.

j = .5m

:

"now twice as old as he was when Mary was three years older than he is now,"

j = 2(j+3-d)

j = 2j + 6 - 2d

j - 2j = 6 - 2d

-j = 6 - 2d 

replace d with (m-j)

-j = -2(m-j) + 6

-j = -2m + 2j + 6

-j - 2j = -2m + 6

-3j = -2m + 6

-3j = -2m + 6

replace j with .5m

-3(.5m) =-2m + 6

-1.5m + 2m = +6

.5m = 6

m = 12 yrs is Mary's present age, then 6 yrs is John's age

:

:

See of that checks out

"John is now twice as old as he was when Mary was three years older than he is now(that's 9) ,

6 = 2(9 - 6)