"EXAMPLE 1";

Clear["Global`*"]

"Fixed values"; Va=2;Ka=5;Vb=7;Kb=3;Vc=5;Kc=10; Vd=3; Kd=0.3;Ve=3;Ke=2;Vf=2;Kf=1;

"Unknowns values";

" a;b;c;d;e;f ";

NSolve[b==Kb*Va*a/(Vb*Ka+(Vb-Va)*a) &&c==Kc*Vb*b/(Vc*Kb+(Vc-Vb)*b)&& d==Kd*Vc*c/(Vd*Kc+(Vd-Vc)*c)&& e==Ke*Vd*d/(Ve*Kd+(Ve-Vd)*d)&& f==Kf*Ve*e/(Vf*Ke+(Vf-Ve)*e)&&

a+b+c+d+e+f==120 && a>0 && b>0 && c>0 && d>0 && e>0 && f>0 ,{a,b,c,d,e,f}]

{{a->90.6943,b->1.11402,c->6.10566,d->0.514849,e->3.43233,f->18.1389}}

____________________________________________________

"EXAMPLE 2";

Clear["Global`*"]

"Fixed values";

Va=2;a=90.6943;b=1.11402;Kb=3;Vc=5;c=6.10566;d=0.514849;Kd=0.3;Ve=3;4323; Vf =2; Kf =1;f=18.1389;

"Unknowns values";

" Ka; Vb; Kc; Vd; Ke ";

NSolve[b==Kb* Va *a/(Vb*Ka+(Vb-Va)*a)&& c==Kc*Vb*b/(Vc*Kb+(Vc-Vb)*b)&&

d==Kd*Vc*c/(Vd*Kc+(Vd-Vc)*c)&& e==Ke*Vd*d/(Ve*Kd+(Ve-Vd)*d)&& f==Kf*Ve*e/(Vf*Ke+(Vf-Ve)*e)&&

Ka >0 && Vb >0 && Kc >0 && Vd >0 && Ke >0,{ Ka, Vb, Kc, Vd, Ke }]

{{Ka ->4.99999,Vb ->6.99999,Kc ->10.,Vd ->3.,Ke ->2.}}

____________________________________________________

"EXAMPLE 3";

Clear["Global`*"]

"Fixed values";

Ka=4.99999;a=90.6943;Kb=3;Vb=6.99999;Vc=5;c=6.10566;Vd=3;d=0.514849;e=3.43233; Ke =2; Vf =2; Kf =1;

"Unknowns values";

" Va;b; Kc; Kd; Ve;f ";

NSolve[b==Kb* Va *a/(Vb*Ka+(Vb-Va)*a)&& c==Kc*Vb*b/(Vc*Kb+(Vc-Vb)*b)&&

d==Kd*Vc*c/(Vd*Kc+(Vd-Vc)*c)&& e==Ke*Vd*d/(Ve*Kd+(Ve-Vd)*d)&&

f==Kf*Ve*e/(Vf*Ke+(Vf-Ve)*e)&&

a+b+c+d+e+f==120 &&

Va>0 &&b>0 && Kc >0 && Kd >0 && Ve >0 && f>0,{Va,b, Kc, Kd, Ve,f}]

{{Va->2.,b->1.11402,Kc ->10.,Kd ->0.3,Ve ->3.,f->18.1388}}

____________________________________________________

"EXAMPLE 4";

Clear["Global`*"]

"Fixed values";

Va =2; Ka=5; Vb=7;Kb=3; Vc=5;Kc=10; Vd=3; Kd=0.3;Ve=3; Ke=2;Vf=2;Kf=1;a=90.695;

"Unknowns values";

" b;c;d;e;f ";

NSolve[b==Kb* Va *a/(Vb*Ka+(Vb-Va)*a)&&

c==Kc*Vb*b/(Vc*Kb+(Vc-Vb)*b)&& d==Kd*Vc*c/(Vd*Kc+(Vd-Vc)*c)&&

e==Ke*Vd*d/(Ve*Kd+(Ve-Vd)*d)&& f==Kf*Ve*e/(Vf*Ke+(Vf-Ve)*e)&&

b>0 && c>0 && d>0 && e>0 && f>0,{b,c,d,e,f}]

{{b->1.11402,c->6.10566,d->0.514849,e->3.43233,f->18.139}}