What does "Eleventy-seven" mean?

I came across the following phrase in a story (set in Australia):

So the fact that I'm forty-five and you're eleventy-seven means nothing to me. If other people have a problem with that, then it's their problem, not ours.

The character is obviously talking about age difference, but is "eleventy-seven" translate to an actual number? Or is it an Australian colloquialism for "really old"?

I tried to search for the phrase, but all I found were pages about a musical group of the same name :)

It's either a real number

110, It is also known as "eleventy", a term made famous by linguist and author J. R. R. Tolkien (Bilbo Baggins celebrates his eleventy-first birthday at the beginning of The Lord of the Rings) and derived from the Old English hund endleofantig. When the word eleventy is used, it may indicate the exact number (110)

Therefore using extrapolation we can assume the author meant 117.

OR

an example of an indefinite (or exagerated) number

inexact terms of indefinite size, used for comic effect, for exaggeration, as placeholder names, or when precision is unnecessary or undesirable.

In The Fellowship of the Ring, Bilbo Baggins was 111 years old and he called it "eleventy-one".

“Today is my one hundred and eleventh birthday: I am eleventy-one today!”

So if the speaker is serious, it would make sense to infer eleventy-seven means 117. But since this is not a normal way of speaking about the number 117, and because people don't often reach 117 years old (or, if they do, it IS significant), it's hard to tell if the speaker literally means 117 or just means "some big number that is much higher than 45". You'll have to determine that from the rest of the story.

From Urban Dictionary:

An imaginary number to be used when you have lost count of something and you need to verbally state a quantity.

In this case, the speaker is using "eleventy-seven" as an arbitrary number; the point is, the age-gap between the speakers is large, but he doesn't care. He could have gotten the same effect by using a number much larger or smaller than her actual age:

The fact that I'm forty-five and you're seven means nothing to me.

The fact that I'm forty-five and you're 120 means nothing to me.

Using a made-up number adds a bit of sarcasm/humor, emphasizing the point that he doesn't care about her age.

I've heard "eleventeen," "threlve," and "a zillion/dillion/gajillion" used as humorous-sounding made-up numbers in similar contexts before. (A friend of mine always used to offer me "threlve doll-hairs" for whatever I currently had in my hand)

My American father has used this word all my life. He would pronounce it more like "Leb-in-dy seven" so as to emphasize that it was a fake number. He would always use it when someone asked him how old he was, or if he was describing how much effort he put into something he didn't want to do. "I must have scooped eleventy seven dog poops..." -- something like that

His grandfather was a southern American born cowboy type who ran farms and bred horses, and his great-grandfather was English. He definitely learned this phrase from his side of the family.