"The girl decided not to answer the long letter."
Translation:Pigen besluttede ikke at besvare det lange brev.
Yes, I would like to know this as well. "Pigen besluttede ikke at besvare..." seems to me that it could also be translated as "The girl didn't decide to answer..", which has a slightly different meaning.
coming from someone with English as her first language, that's what we would expect. The Danish construct seems to be almost too straightforward! Literally decided + not + to + reply
I also think that 'pigen besluttede at ikke besvare..' is the correct answer.
I translated 'Pigen besluttede at ikke besvare det lange brev' and it was marked wrong. I still think I might be right. The English sentence starts 'The girl decided ...' - so she did decide, and when you ask what she decided it is 'not to answer the letter'. The suggested Danish solution starts 'Pigen besluttede ikke ...', so she did not decide about it (she might ponder over it and decide later). However: neither English nor Danish is my native language, I was just analyzing the sentences from a mathematical point of view.