Time weighted number of shares

Hello all,

I want to calculate what is the time weighted number of shares I held throughout the month. If you are unfamiliar with the concept, I have made an example in the attached sheet. General idea is, say as of end of last month I held 100 shares. Middle of this month I bought 100 more shares. While as of end of this month I would be holding 200 shares, in reality the time weighted average amount of shares I held were closer to 150.

The problem is I'm having trouble getting that result through one formula. Perhaps you guys can help in that regard. (the "x"s need to be the output location)