Although investing all at once works best when stock prices are rising, dollar$-$cost averaging can be a good way to take advantage of a fluctuating market. Dollar$-$cost averaging is an investment strategy designed to reduce volatility in which securities are purchased in fixed dollar amounts at regular intervals regardless of what direction the market is moving. This strategy is also called the constant dollar plan.

You are considering a hypothetical $$1,200$ investment in a media company's stock. Your choice is to invest the money all at once or dollar$-$cost average at the rate of $$100$ per month for one year. Assume that the company allows you to purchase "fractional" shares of its stock.

$($a$)$

If you invested all of the money in January and bought the shares for $$12$ each, how many shares could you buy?

shares