Investors valued ride$-$hailing giant Lyft at more than $$24$ billion at the time of its $2019$ IPO. The dual$-$class company had $273,097,591$ shares of Class A common stock and $12,779,709$ shares of Class B common stock outstanding. The company's co$-$founders, Logan Green and John Zimmer, collectively own $1,369,182$ Class A shares and all $12,779,709$ Class B shares. Although the equity investments represented by one share of Class A common stock and one share of Class B common stock are identical, their control rights are different. Class A holders are entitled to one vote per share and Class B holders are entitled to $20$ votes per share.

a$.$ What percentage of equity interest do the founders, CEO Logan Green and President John Zimmer collectively own?

b$.$ What percentage of control $($i$.$e$.$ voting$)$ rights do Logan Green and John Zimmer collectively own?

c$.$ Imagine that one year after its IPO, Lyft conducts an equity offering and sells an additional $100$ million Class A shares to outside investors. What impact will the sale of these additional shares have on the percentage of equity investment and control rights collectively held by the founders, assuming that they do not purchase new Class A shares or sell any shares they hold prior to the new equity offering?

d$.$ Now imagine that in addition to the $100$ million shares Lyft sold in part c$,$ Green and Zimmer also sold $1,369,182$ of their Class A shares to outside investors. Leaving only the Class B shares, what percentage of the equity investment and control rights are held collectively by the founders?