The current stock price of Alcoa is $70 and the stock does not pay dividends. The instantaneous riskfree rate of return is 6%. The instantaneous standard deviation of Alcoa's stock is 40%. A put option on this stock with an exercise price of $75 and an expiration date 30 days from now. According to the Black-Scholes OPM, you should hold __________ shares of stock per 100 put options to hedge your risk .

a. 30 b. 34 c. 69 d. 74

The answer is 69. I need a DETAILED explanation of the math behind how to get this answer please. I need to know every part of this equation.