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The system of equations is as follows:

{(fmale + ffemale)/200 > (fmale + ffemale + smale + sfemale)/500, 
 fmale == 0.5*fNAN, ffemale == 0.7*fNV, fNAN + fNV == 200, 
 smale == 0.6*sNAN, sfemale == 0.9*sNV, 
 sNAN + sNV == 300}, {fmale, ffemale, smale, sfemale}

All variables are positive integers

I tried FindInstance, Reduce, etc. can not be solved. I need to ask for all solutions, there may be 36.

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  • $\begingroup$ Something to adjust in view of Solve[{(fmale + ffemale)/200 > (fmale + ffemale + smale + sfemale)/ 500, fmale == 1/2*fNAN, ffemale == 7/10*fNV, fNAN + fNV == 200, smale == 6/10*sNAN, sfemale == 9/10*sNV, sNAN + sNV == 300}, {fmale, ffemale, smale, sfemale}] which results in {}. $\endgroup$ – user64494 Jul 5 at 7:57
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Search for all variables.

fi = FindInstance[{3 (ffemale + fmale) > 2 (sfemale + smale), 
2 fmale == fNAN, 10 ffemale == 7 fNV, fNAN + fNV == 200, 
5 smale == 3 sNAN, 10 sfemale == 9 sNV, sNAN + sNV == 300, 
fmale > 0, ffemale > 0, smale > 0, sfemale > 0, fNAN > 0, fNV > 0, 
sNAN > 0, sNV > 0}, {fmale, ffemale, smale, sfemale, fNAN, fNV, 
sNAN, sNV}, Integers, 40]

fi // Length

(*   36   *)

ListLinePlot[#, PlotRange -> {0, 300}, Mesh -> All, 
  GridLines -> Automatic] & /@ 
Evaluate[{fmale, ffemale, smale, sfemale, fNAN, fNV, sNAN, sNV} /. 
fi]
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