Question 419287
Let a = Ann's age today
Let b = Bill's age today

We know that in two years (when Ann is a + 2 and Bill is b + 2) that Ann will be twice Bill's age, that is:

a + 2 = 2(b + 2)
Simplifying this equation, we have:
a + 2 = 2 b + 4
a = 2b + 2

We know that three years ago (when Ann was a - 3 and Bill was b - 3) that Ann was three times Bill's age, that is:

a - 3 = 3(b - 3)
Simplifying this equation, we have:
a - 3 = 3b - 9
a = 3b - 6

Putting the two equations together, we have:
2b + 2 = 3b - 6
2 = b - 6 (subtracting 2b from both sides)
8 = b  (adding 6 to both sides)

So today, Bill is 8 and Ann is 18.

Answer:  Bill is 8 today.