Translation:They sing and play music for money.
за = for, they sing and dance for money, so they are doing this for the sake of earning money. для = for (a thing, person) If you use для in this sentence it means that they are singing and dancing in front of money. Maybe because the money forced them to do it, so they are doing this.
для is used when you will give a gift to someone, like этот подарок для тебе
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The English translation here is extremely strange. Normally we would say they play music and sing for money. The way this is written it says they sing music and they play music. While I suppose that is technically correct, it's very awkward to put sing and play in this order.
I have never understood why the Russian language has prepositions, if the purpose of the cases is to negate said prepositions.
Could someone explain to me in what contexts NEED prepositions. This is my only problem at the moment and it would help me a lot if I could know.
Thanks in advance!
за деньги seems idiomatic. I tried plugging a number of different nouns into this sentence in an on-line translator, and if the payment was something besides money, "for" was translated as дла, e.g., Они поют для еды = "they sing for food".
As a result, I'm not sure that the usual considerations regarding the case of objects of за. This seems like a special instance. But without more information, it's impossible to say.