In the first chapter of The Lord of the Rings, Bilbo is about to reach the age of eleventy-one, in, 'a rather curious number', and at his birthday party, his announcement 'I am eleventy-one today' is met with cheers from the assembled guests. In English there are other invented terms for numbers representing tens, most famously umpty, which is now almost forgotten, but on which was based the very common word umpteen. It would be easy to see this as a piece of whimsical fancy based on Lewis Carroll logic: if we can count to ninety, why not eleventy?
But as always with Tolkien, the roots go deeper, and are planted in the reality of the culture of the ancient world. In Old English, the next two tens after hund 'hundred' were hundendlufontig and hundtwelftig: the hund- was a prefix, which also occurred in hundeahtatig 'eighty' and hundnigontig 'ninety'; if we remove the prefix, we get -endlufontig 'eleventy' from endlufon or endleofon 'eleven' and -twelftig 'twelfty'. Why did the Anglo-Saxons count up to 'twelfty'? The answer lies in an ancient system of counting in twelves; much later, at the end of the Middle English period, certain commodities, such as fish, were counted in 'hundreds' that actually contained six score or 120, and this was known as the 'great hundred' or 'long hundred' (OED: hundred n. and a., sense 3). That this probably goes back to ancient times is shown by the fact that in Old Norse 100 was tiu tigir'ten tens', 110 was ellifu tigir 'eleven tens' (exactly parallel to eleventy), and 120 was hundrad 'hundred'. There are even said to be ordinal numerals titugandi and ellifu-tugandi 'tentieth' and 'eleventieth'.
Similarly, the OED shows that, from around 1400, many commodities were reckoned by the gross (OED: gross n.3), which signified 12 dozen (144). We know that the hobbits used this reckoning from another place in the same chapter, where we are told that the invitations to the special family dinner party were limited to twelve dozen, 'a number also called by the hobbits one Gross, though the word was not considered proper to use of people' — Bilbo offends his guests later in the speech already referred to, by doing just that. The party is even punningly described as 'an engrossing entertainment', although the sentence containing this phrase no longer contains the mention of '144' present in the early draft (HMEVl. 23), so many readers miss the pun.
Tolkien is imagining, as with many other matters, that the hobbits continued a practice used by our forefathers. But he presumably also knew that the OED has an entry for the similarly formed word eleventeen meaning 'twenty-one', which was used by a 17th-century writer named George Wither (and also revived in a Victorian farce by Charles Selby in 1858}. It is also quite probable that he had come across this gloss for the Icelandic word ellefu-tiu in Cleasby and Vigfusson's Icelandic-English Dictionary (1874): '"eleventy" (i.e. one hundred and ten),,..frequent in reckoning by duodecimal hundreds'.
The Ring of Words