Recently, one of my chavrusos raised a question that seemed like a really difficult problem. Towards the end of Deuteronomy (31:2, 34:7) the Torah tells us that when Moses died, at the end of the forty years in the wilderness (Deut.1:3), he was one hundred and twenty years old. This would mean that Moses was 80 years old at the time that he and the Jewish people left Egypt and, in fact, we read Exodus 7:7 that "Moses was eighty years old and Aaron was eighty-three years old when they spoke to Pharaoh."
The problem, however, is that this verse is written before the plagues begin later in the same chapter. While Scripture itself is vague as to the exact amount of time that passed from the beginning of the first plague to the last, it was clearly not a matter of a few weeks. Indeed, Jewish tradition (recorded in the Mishna, Eduyos 2:10) is that the ten plagues took place over a period of twelve months. If Moses was eighty years old at the beginning of this period, then he would have been eighty-one years old at the time of the exodus, which would make him 121 years old at the end of the forty years in the desert. (Exactly the same question can also be asked regarding Aaron.)
This would seem to be an obvious problem. In fact, in my opinion, the first hint to the solution is precisely that the problem is too obvious. All the major commentaries - who typically address issues of this sort - ought to be noting the issue, yet, to my knowledge, it is completely ignored by all the major commentaries.
(רק מצאתי שהחת"ם סופר דחק לתרץ בשני אופנים, אחת בשו"ת ח"ו סי' כט, ואחת - שלא זכיתי להבין על בוריו - בדרשות חת"ם סופר לפרשת שקלים, ח"א דף קיז:)
When we encounters an apparently obvious problem that is apparently ignored by the commentaries, this is usually an indication that the source of the problem is actually a more basic flaw in our understanding of the material. In this case, it would seem that to the commentators, the "solution" was so self-evident that the "problem" never even presented itself. While this might sound self-defeating, it actually helps us a great deal in resolving the issue. If the solution was that self-evident, then the answer should be right there on the page, where any competent reader can see it.
With this in mind, we can return to the text in Exodus 7 and attempt to read it as the classical commentators would have read it. The first thing that we need to bear in mind, which is often overlooked by modern readers, is that the text of the Torah is divided into paragraphs. These paragraphs will be familiar to anyone who has ever read from a Torah scroll. These paragraphs are called פרשיות (parshiyos), and the division of these פרשיות was passed down to us in the written text of the Torah as given to us by Moses as he received it from Hashem. Like paragraph breaks in any text, these פרשיות are essential to a proper understanding of the Torah.
(By contrast, the conventional division of the text the Torah into chapters (פרקים) is not only not of Divine origin, but it is not even of Jewish origin and frequently does not reflect the traditional Jewish understanding of the text.)
When we look at the text in Exodus 7, we find that the verse we are discussing is the final verse of a paragraph. The paragraph in full (7:1-7) states:
And Hashem said to Moses: 'See, I have made you a master over Pharaoh; and Aaron your brother brother shall be your spokesman. You shall speak all that I command you; and Aaron your brother shall speak to Pharaoh, that he shall send the children of Israel out of his land. And I shall harden Pharaoh's heart, and I shall multiply My signs and My wonders in the land of Egypt. And Pharaoh will not listen to you, and I shall place My hand upon Egypt, and I shall bring out My hosts, My people the children of Israel, from the land of Egypt with great judgments. And Egypt shall know that I am Hashem, when I stretch forth My hand upon Egypt, and I bring out the children of Israel from among them.' And Moses and Aaron did so; as Hashem commanded them, so they did. And Moses was eighty years old, and Aaron eighty-three years old, when they spoke to Pharaoh.
We see in this paragraph God instructing Moses in a general sense of how he would interact with Pharaoh, and giving Moses an overview of the entire process of the Exodus, covering the entire period of the plagues, followed by the actual Exodus from Egypt. In regard to this overview of the entire Exodus process, the Torah, speaking from the perspective of the reader, tells us that, when it was all over, Moses and Aaron had done all that God had commanded them. It is in this context, speaking after the exodus, that the Torah says, "And Moses was 80 years old... when they spoke to Pharaoh."
Thus, from the context of the verse it seems clear that the verse is speaking of the age of Moses and Aaron, not at the beginning of the plagues, but at the conclusion of their talks with Pharaoh just before they left Egypt. If, instead of being the last verse of the previous paragraph, the verse had been the first verse of the next paragraph, which describes Moses and Aaron actually meeting with Pharaoh, then the problem would present a serious difficulty. However, as the conclusion of the previous paragraph, which is describing the course of future events, the problem disappears.