SOLUTION: Ann and Bill are both celebrating their birthday today. Two years from now Ann will be twice as old as Bill, while 3 years ago Ann was three times as old as Bill. How old is Bill n

Question 419287: Ann and Bill are both celebrating their birthday today. Two years from now Ann will be twice as old as Bill, while 3 years ago Ann was three times as old as Bill. How old is Bill now?

Answer by duckness73(47) (Show Source): You can put this solution on YOUR website!
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.
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