I'm not sure that it is very natural to say "the sum of food".... to me it sounds like an oddly formalistic thing to say. You would rather say "the amount of food" IMO.
It isn't really natural to say "Summen af mad" in Danish. One would rather say "Mængden af mad" ("The amount/quantity of food".
I would say that the 'the amount of' is more common, but that 'the sum of' is increasing in usage (this is admittedly anecdotal). It of course starts with numbers, but by metaphorical extension it can expand it's base.
so now we have summen, antal, and mænde which mean pretty much the same thing. anyone have a clear and concise explanation of when to use each?
Well, "summen" literally means the sum of, while "mængden" means the amount of. You use it like you would those two english phrases.
If I said 'Summen af mad er ikke tilstrækkelig', would that make sense to a Danish speaker?
Well, yeah, but it's not anything i would say in real life, just like i wouldn't say "the sum of food" in english
If you would not say it in real life then it does not make sense! Why are we learning something you should never say?
I really don't know! I mean, i would understand what you were saying, but it would probably be better to say "Mængden af mad er ikke tilstrækkelig" - or simply "Der er ikke mad nok"
"The amount of food is not enough" is properly what is meant. It could also be (strange context) that the humming of cooking food is not loud enough, but I've never imagined that'd be an issue...
"The amount of food is insufficient" is accepted. A little less awkward translation.
The word "summen", 'the sum', makes no sense when talking about food - you don't quantify food with numbers, unless you talk about "the number of burgers". It's like "the number of money..." -doesn't work.
"Tilstrækkelig" and "nok" would be just fine using, if the food is an amount, "Mængden".