How many restaurants a big burger chain runs in the US

Estimate how many outlets a leading hamburger chain operates across the United States.

On the order of 10,000 to 15,000. One route: about $330$ million people, perhaps $1$ outlet per $25{,}000$–$30{,}000$ residents for the dominant chain (urban density is higher, rural lower), giving roughly $11{,}000$–$13{,}000$. Cross-check with demand: if a typical outlet serves about $2000$ customers a day, and around $8\%$ of Americans visit on a given day, you get a similar figure. The real figure for the largest chain is about $13{,}000$.