"...the steelmakers let on not only about the good feeling..." To let on about something means to reveal some personal information or to betray (give away) a secret. "Don't let on..." means you
shouldn't tell anyone what you've heard. This is a classic phrasal verb, because if you translate it literally you get ,,dovoliť na", which doesn't make sense, so you have to understand it as a
whole phrase meaning ,,prezradiť niečo". Other examples of "let" as a phrasal verb are "to let up" (decrease your effort, slow down), "to let out" (extend the waistband of your trousers or skirt),
"to let down" (to disappoint or fail somebody), or "to let off" (light a firework, or expel wind from your behind). "To let in" is not a phrasal verb though; it means literally ,,dovoliť vojsť" or
,,pustiť dnu", and likewise "let out" can mean simply ,,pustiť von" - Who let the dogs out?!
I've been asked to explain the difference between "She's been to Paris" and "She's gone to Paris". One way to find the difference is to say the sentences in other words: she has visited Paris (at
least) once in her life, compared with: she is visiting Paris now. Another difference lies in the answers to the question "Where is she now?" In the first case, she's not in Paris, and most likely
at home now; in the second, she's not here, but most likely in Paris now. Then there are the answers to the question: "Does she know Paris?" In the first case the answer is yes, possibly quite well
(lebo už tam bola aspoň raz), whereas the second is maybe yes, maybe no, but she will soon (lebo teraz je tam). The same thing in both sentences is that you have to say "to Paris", because in both
cases there is the idea of movement, of traveling to a destination.