In this case, it depends on what you put after "beaucoup":
- a noun: beaucoup de choses à manger (a lot of/many things to eat)
- a verb: beaucoup à manger (a lot/much to eat)
This would work for any expression of quantity (peu, un peu, plus, moins, autant...).
Otherwise, after an adjective (facile, difficile, possible, impossible, nécessaire, inutile...), the choice of "à" or "de" will depend on the subject:
- impersonal: il est impossible de manger maintenant (it is impossible to eat now)
- real: cette viande est impossible à manger (this meat is impossible to eat)
I would still say that the idiomatic use of "plenty" in this context in English justifies its acceptance as a correct answer. It is technically true that plenty means "more than enough" while a lot simply means "a large amount", without reference to adequacy or inadequacy (you can say, without contradiction, 'a lot, but not enough', but not, 'plenty, but not enough'), but these meanings overlap in usage, and in this context are virtually synonymous. I hope this isn't "reporting a mistake"; though where does one inquire as to allowing an answer if not in the comments?