11. (15 points) A store makes a profit of 9 yuan from selling one fountain pen, and the purchase price of a small teddy bear toy is 2 yuan. Once, the merchant adopted a "buy 4 fountain pens and get one small teddy bear toy for free" promotional pack, and made a total profit of 1922 yuan. How many fountain pens were sold at most in this promotion?
【Analysis】According to the problem, "buy 4 pens and get a small bear toy for free" means that selling 4 pens actually yields a profit of $9 \times 4 - 2$ $= 34$ yuan. To maximize the number of pens sold during this promotion, we need to maximize the number of bundled sales. Therefore, we can determine how many times 1922 is a multiple of 34, which will tell us how many sets of 4 pens can be sold, and then calculate the maximum number of pens sold. Based on this, we can solve the problem.

【Solution】Analysis: To maximize the number of pens sold during this promotion, we need to maximize the number of bundled sales.
$$
\begin{array}{l}
1922 \div (4 \times 9 - 2) \\
= 1922 \div 34 \\
= 56 \text{ (times) } \cdots 18 \text{ (yuan); } \\
18 \div 9 = 2 \text{ (pens); } \\
56 \times 4 + 2 \\
= 224 + 2 \\
= 226 \text{ (pens). }
\end{array}
$$

Answer: The maximum number of pens sold during this promotion is 226 pens.