http://www.analog.com/UploadedFiles/Data_Sheets/SSM2211.pdf

On pg. 16 they are deriving power efficieny as the difference between the power delivered by the supply and the power delivered to the load by the amp. Equations 3 and 5 are of interest.

The text explains that equation 3 and 5 are expressed in terms of peak voltage. This makes sense for equation 3 which is really the RMS value of power expressed in terms of peak voltage. A simple algebra manipulation.

I do not see this in equation 5. They are stating they are expressing the average current as a peak voltage, but the equation itself is literally the average value of a sinusiodal current waveform, rather than an RMS waveform expressed as a peak signal similar to equation 3.

Are they not mixing apples and oranges here? RMS and Average values?

It seems they are trying to obtain similar variables, Vpeak, to derive equation 6. and 7 I am not questioning the validity of the actual average value equation, just the purpose of using it to derive a power caluation.