A manufacturing plant makes $10$-inch, $9$-inch, and $7$-inch frying pans. During a certain day, the number of $10$-inch frying pans that the manufacturing plant makes is $4$ times the number $n$ of $9$-inch frying pans it makes, and the number of $7$-inch frying pans it makes is $10$. During this day, the manufacturing plant makes $100$ frying pans total. Which equation represents this situation?