Yosef stood before Pharaoh when he was 30 years old. (Breishis 41:46) Following that there was seven years of plenty then two years of famine. (Breishis 45:6) At that time Yaakov and his family came down to Egypt. [Breishis 46:6]
How old was Yosef when Yaakov came down to Egypt?
30 + 7 +2= 39 years old
Yosef is six years old when his father Yaakov left the house of Lavan. [Breishis 30:25, 31:41]. The destruction of Schem takes place two years after that. [Rashi to Breishis 28:9] The Midrash tells us that Levi was 12 years old at the time of the incident at Schem. [Rabbeinu Bachya Breishis 34:25] How much older was Levi than Yosef?
12 – (6 + 2) = 4 years older
How old was Levi when he came down with Yaakov to live to Egypt?
39 + 4 = 43 years old
Levi lived to the age of 137. [Shemos 6:16] How many years did he live in Egypt?
137 – 43 = 94 years living in Egypt
The Jews would remain in Egypt for another 210 years. (Rashi Shemos 12:40) While the Jews were in Mitzryim for 210 years, according to one opinion, the actual enslavement did not begin until the last of Yaakov son’s (i.e. Levi) died. (Seder Olam Chapter 3) How many of the 210 years living in Egypt were years of slavery?
210 – 94 = 116 years.