Notam cele trei numere cu x,y si z. Stim ca x+y+z=345, iar din al doilea enunt putem deduce urmatoarele egalitati:
[tex]x+\frac{25}{100}*x=y+\frac{50}{100}*y=z+\frac{20}{100}*z[/tex] <=>
[tex]\frac{125}{100}*x=\frac{150}{100}*y=\frac{120}{150}*z[/tex] <=>
125x=150y=120z. De aici incercam sa exprimam cele trei numerele prin unul singur( aici s-a ales sa se scrie toate in functie de z):
x=[tex]\frac{150}{125}*y=\frac{30}{25}*y=\frac{6}{5}*y[/tex]
y=[tex]\frac{120}{150}*z=\frac{12}{15}*z=\frac{4}{5}*z[/tex]
x+y+z=345 <=> [tex]\frac{6}{5}*y+\frac{4}{5}*z+z=345[/tex] <=> [tex]\frac{6}{5}*(\frac{4}{5}*z)+\frac{4}{5}*z+z=345[/tex] <=>
[tex]\frac{24}{25}*z+\frac{4}{5}*z+z=345[/tex] <=> [tex]\frac{44z+25z}{25}=345[/tex] <=> [tex]\frac{69z}{25}=345[/tex] <=> [tex]z=\frac{345*25}{69}=5*25=125[/tex]
y=[tex]\frac{4}{5}*125=4*5=100[/tex]
x=[tex]\frac{6}{5}*100=6*20=120[/tex]
