a+b+c=345
[tex]a+ \frac{25}{100} *a=b+ \frac{50}{100} *b=c+ \frac{30}{100} *c=>
\frac{5a}{4} = \frac{3b}{2}= \frac{13c}{10} [/tex]
[tex] \frac{5a}{4} = \frac{3b}{2} => 10a=12b=> a= \frac{12b}{10}= \frac{6b}{5} [/tex]
[tex]\frac{3b}{2}= \frac{13c}{10} => 30b=26c=> c= \frac{30b}{26} = \frac{15b}{13} [/tex]
Inlocuim in prima relatie si obtinem:
[tex] \frac{6b}{5} +b+ \frac{15b}{13} =345=> \frac{6b*13+65b+15b*5}{65}=345=> 218b= 65*345[/tex]=> b=[tex] \frac{22425}{218} [/tex]=> [tex]a= \frac{26910}{218} , c= \frac{25875}{218} [/tex]
