How to decide the appropriate level of explanation for math in academic papers? In any academic paper dealing at least in part with math, the authors have to make a choice how much explanation to actually give the math.

It can range from pretty much no explanation:


  Given a foobar of 12, a ackbar of 57, and general frobnosticating
  parameter of 9, the resulting nyan level will be 8. 


To belaboring the obvious


  The first three people went into the city. Later, four more people
  went into the city. This meant that seven people had gone into the
  city which is derived by adding the first three people to the next
  four people. We add because people are individual units and moving
  them to a new location neither combines or divides those units.


How does one decide the appropriate level of explanation? Is there any sort of standard that can be appealed to decide when something is clear enough?

The actual background for this question is that I've looked at a paper for a colleague. It is in a non-mathematical subject but does engage in some mathematical reasoning. I think the paper doesn't explain enough, but my colleague disagrees. I have to work at figuring out what calculations were done in the paper and the justification for many of the inferences he draws. That indicates to me that the explanation is insufficient, but is there a less subjective standard I can appeal to?
I find that the choice of how much explanation to give math is generally a three-way negotiation between three factors:


Your estimate of the audience: different communities will need radically different levels of explanation for the same mathematics.  
Adjustment based on the opinions of the reviewers about what needs more or less details
Any length constraints on the paper.


Of this #1 is really the important thing: you really need to understand your audience in order to decide how in-depth to go with your mathematics.

For example, I recently published a paper which spent several pages explaining a mathematical formulation in depth for its target cross-disciplinary audience.  The reviewers requested further expansion of the mathematical explanation (which I was happy to provide).  Were I writing for the community from which the mathematics came, however, I would instead spend several pages explaining the context of the problem, but then the math itself would be covered in just a few sentences.