Using the term Akedah (binding) to refer to the event, Isaac's age at Akedah can be constrained from two related passages:
Paul's statement in Gal 3:17 - reflecting the view in the proto-rabbinic circle of Gamaliel, under whom Paul had studied the Torah - that the Law had come 430 years after God's promise to Abraham and to his offspring. (This statement obviously implies the adoption of the "short soujourn" view of the Israelites' stay in Egypt, i.e. that the 430-year interval of Ex 12:40 began at Gen ch. 15.) Now, Abraham's act of faith mentioned in Gal 3:6 and God's promise to Abraham and to his offspring mentioned in Gal 3:16 are in Gen 15:6 and 15:18 respectively, within the event known as "Covenant of the pieces". Therefore we must estimate the time elapsed between Abraham's departure from Haran (Gen 12:4-5) and the promise in Gen 15:18.
Within the "Covenant of the pieces", the prophecy in Gen 15:13 that Abraham's offspring ("seed") would serve and be afflicted for 400 years. The servitude and affliction of Abraham's offspring can be understood to have begun in any of two moments:
at the feast on the day that Isaac was weaned, when Ishmael mocked Isaac (Gen 21:9), or
at Akedah, when Abraham laid the wood of the burnt offering on Isaac (Gen 22:6) and then bound him and laid him on the altar, on top of the wood, and reached out his hand and took the knife to slay him (Gen 22:9-10).
Thus, adopting a convention of denoting a specific moment as LLL.n, where:
LLL are the first 3 letters of Abraham, Isaac, Jacob or the Promise of Gen 15:18,
n is LLL's age at that specific moment if it is a figure, or the number of years that have elapsed from LLL if it is the Promise,
we have the following sequence of events and intervals:
Abr.75. Abraham leaves Haran (Gen 12:4-5).
- a (Time elapsed between Abraham's departure from Haran in Gen 12:4-5 and the promise of Gen 15:18 within the Covenant of the Pieces)
Pro.0 = Abr.(75 + a). Covenant of the pieces (Gen ch. 15): Abraham believes the LORD and receives the 400-year prophecy and the promise.
Pro.(25 - a) = Abr.100 = Isa.0. Isaac is born (Gen 21:2-5).
- b (Isaac's age at the event beginning the 400 years of servitude and affliction of Abraham's offspring prophecied in Gen 15:13)
Pro.(25 + b - a) = Abr.(100 + b) = Isa.b. Beginning of the 400 years of servitude and affliction of Abraham's offspring: either Ishmael mocks Isaac (Gen 21:9) or Abraham offers Isaac in sacrifice (Gen ch. 22).
Pro.(85 - a) = Abr.(160) = Isa.60 = Jac.0. Jacob is born (Gen 25:26).
Pro.(215 - a) = Jac.130. The Sons of Israel enter Egypt (Gen 47:9).
- (215 + a) (Duration of the Israelites' sojourn in Egypt)
Since the Covenant of the pieces must have been before Sarai gave Hagar to Abram as a wife, which happened "after Abram had lived ten years in the land of Canaan" (Gen 16:3):
0 <= a <= 10
Since the 400 years of servitude and affliction of Abraham's offspring prophecied in Gen 15:13 ended at Exodus, we have:
400 = 430 - (25 + b - a)
0 = 30 - 25 - b + a
b = 5 + a
Thus we have:
0 <= a <= 10
5 <= b <= 15
where the values of both variable time intervals move in tandem from left to right within their respective 10-year ranges. Accordingly, the range of the duration of the Israelites' soujourn in Egypt, 215 + a, is from 215 to 225 years.
Since 5 years is way too advanced an age for weaning, the event beginning the 400 years of servitude and affliction of Abraham's offspring prophecied in Gen 15:13 was Akedah (which was always my preferred option, since carrying the wood for the burnt offering and then being bound and laid on the altar and about to be sacrificed was real servitude and affliction, as opposed to just being mocked). We can further constrain Isaac's age at the event by noting that he had to be able to carry the wood of the burnt offering on top of himself, which IMO imposes a realistic minimum age of 8 years. Thus we arrive at the ranges:
3 <= a <= 10
8 <= b <= 15 (Isaac's age at Akedah)
218 <= duration of the Israelites' sojourn in Egypt (215 + a) <= 225.