mucho/muchas

Question

Lina sonríe ________.Lina smiles a lot.I thought the answer were plural, muchas for feminine. However, the answer is mucho. May I know what is the reason.

Answer

Hola Cathy,
"mucho" here is not an adjective, it is an adverb, therefore it is invariable. We always use it in the same form "mucho" when saying "a lot"
To use it as an adjective (mucho, mucha, muchos, muchas) it'd need a noun to refer to (a lot of something, lots of something):

He bebido mucho vino.
I have drank a lot of wine.
He comido mucha paella.
I have eaten a lot of paella. 
Hay muchos pájaros.
There are lots of birds.
He visto muchas películas.
I have seen lots of films.

I hope this clarified it.
Saludos