# How to solve all the solutions of this restricted system of equations?

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.

• 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 {}. Jul 5, 2020 at 7:57

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]