In the LOTR movies, Gandalf remarks that Bilbo's adventures ended 60 years before his eleventyfirst birthday.
Aragorn tells Eowyn that he is 87, so would that place him at 27 during the events of The Hobbit?
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No, your math is a bit off, but it's mostly the movie's fault. According to the information from the various novels/appendices, etc:
The problem here is that the plot in the novels, and the movies, skips pretty quickly from Bilbo's birthday party to Frodo leaving the Shire. However, in the novels it's made clear that a lot of time has passed between those two events, while the movies mostly gloss over that.
That's not to say that the movies are different; keep in mind everything that happened off-screen between those two events. Galdalf travelled across Middle-earth looking for information about the One Ring, and he and Aragorn even tracked down Gollum after Sauron captured and tortured him. That leaves an 18-year-gap gap that's only hinted at in the movies, but does make the Aragorn's age match up correctly at the various points.