I believe the ages to be “space markers” or ‘counters’, if you will. There are countless missing generations and this was a way to get from one known individual to the next known individual without having to take into account all the missing generations between the two.
Aside from being space markers/counters for missing generations from one known (even if known in name only) individual to the next, there is another possibility for the ages referenced. I don’t recall exactly where i got this, but…
We must keep in mind that this is not a firsthand account, but rather a record of ancestral tradition.
There are examples of lists of important people with extraordinary numbers listed as their ages in multiple examples from the Ancient Near East; the Biblical tradition is not the first. So there is a precedent for the Old Testament to do this.
The Sumerians and other Mesopotamian peoples (since at least 3100 BC) used a sexagesimal numbering system, which means that it was base 60, instead of our base 10.
The biggest issue with Mesopotamian numbers, however, is the idea of sacred numbers. Some numbers had a symbolic meaning beyond their mathematical meaning, and therefore were numerological rather than numerical in some contexts, meaning that its symbolic value would be used rather than its mathematical value.
Now, what connection does this have to the Biblical chronologies? The numbers are based on the Mesopotamian system of numbers. All the ages in the Genesis genealogies fall into two categories: numbers divisible by 5 (ending in 5 or 0), and multiples of 5 with the addition of 7 (or two 7s). 5 years = 60 months. The final digits are always 0, 7, 5, 2, and 9. 2 because 5+7 = 1 2 , and 9 because 5+7+7 = 1 9 . The odds are astronomical that there would not be a number in the list that did not match. Therefore, we have a lot of indications that these are symbolic numbers, based on a very different number system; however, we don’t really know what meaning these numbers may have had to the original tellers/keepers of these genealogies.
Additional evidence for these being symbolic rather than real can be seen in the fact that many of the patriarchs’ ages overlap significantly and impossibly according to the narrative. Additionally, there are different numbers among various ancient translations of the text (specifically the Hebrew Masoretic Text and the Greek translation of the Old Testament, the Septuagint).
Again, looking specifically at the ages of the Patriarchs, we can see that this is a list that has correlations with other similar lists. If you take the list of the ages of the Sumerian pre flood kings, and assume that instead of being in a sexigesimal system (base sixty) they are instead part of a base ten system, you end up with a list of ages that are equivalent to the Biblical one, albeit rounded to the nearest ten. As time went by, many of these cultures went through a number of different number systems, as well as different ways of representing numbers.