A factory makes $9$-inch, $7$-inch, and $4$-inch concrete screws. During a certain day, the number of $9$-inch concrete screws that the factory makes is $5$ times the number $n$ of $7$-inch concrete screws, and the number of $4$-inch concrete screws is $22$. During this day, the factory makes $100$ concrete screws total. Which equation represents this situation?