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Let x be the number of months.
Bradley will have 23 + 4x bumper stickers.
Ryan will have 9 + 6x bumper stickers.
To find when they are equal, set 23 + 4x = 9 + 6x.
Subtracting 4x from both sides, we get 23 = 9 + 2x.
Subtracting 9 from both sides, we get 14 = 2x.
Dividing both sides by 2, we get x = 7.
So after 7 months they will have the same number of bumper stickers. Answer: \boxed{7}.