If you do something profitably, two things can be true, and students need both.

If you do something profitably如果你 profitably 地做某件事 two things can be true可能有兩種意思 and students need both學生兩種都要懂

First, it can mean “in a way that makes a profit”: they sold the land profitably.

First第一 it can mean "in a way that makes a profit"可以指「用會賺錢的方式」 they sold the land profitably像是他們把土地賣得有獲利

Second — and this is very common — it can mean “in a useful way, so that you get something good out of it,” even when no money moves. You can spend an afternoon profitably by reviewing notes. You can look at old mistakes profitably.

Second, and this is very common第二個意思也很常見 it can mean "in a useful way, so that you get something good out of it,"是指「用有益的方式，讓你從中得到好處」 even when no money moves即使完全沒有牽涉到錢 You can spend an afternoon profitably你可以有意義地度過一個下午 by reviewing notes像是拿來複習筆記 You can look at old mistakes profitably你也可以有益地檢視過去的錯誤

Though actually, the “useful result” sense is older and wider than the money sense, but business writing usually wants the money. The word is a little formal in both uses; friends more often say “It was worth it” or “We made money.”

Though actually不過其實 the "useful result" sense is older and wider than the money sense「有益處」這個意思比「賺錢」這個意思更古老也更廣 but business writing usually wants the money不過商業文章通常想講的是錢 The word is a little formal in both uses這個詞不管哪種用法都有點正式 friends more often say "It was worth it" or "We made money."朋友之間更常說「這很值得」或「我們賺到了」