A bakery sells a variety of cookies in two different sizes: small and large. The ratio of small cookies sold to large cookies sold is 3:2. After selling 120 small cookies, the bakery has sold twice as many large cookies as small cookies, and the total sales of large cookies amount to $480. If the price of each large cookie is the same across all sales, determine the price of each large cookie.
Let the price of each large cookie be represented as $p$. Formulate the necessary equations based on the given information and calculate $p$.