Folosim produsul mezilor este egal cu produsul extremilor.
Il scoatem pe y in functie de x:
[tex]\frac{x}{y}=\frac{15}{14}\Leftrightarrow 14x=15y\Leftrightarrow y=\frac{14}{15}x [/tex]
Il scoatem pe y in functie de z:
[tex]
\frac{y}{z}=\frac{15}{14}\Leftrightarrow 14y=15z\Leftrightarrow y=\frac{15}{14}z[/tex]
Egalam cele doua:
[tex] \left \{ {{y=\frac{14}{15}x} \atop {y=\frac{15}{14}z} \right. \Leftrightarrow \frac{14}{15}x=\frac{15}{14}z\Leftrightarrow 14\cdot14x=15\cdot15z\Leftrightarrow 196x=225z\\
\Leftrightarrow z=\frac{196}{225}x[/tex]
Inlocuim y si z si obtinem o ecuatie cu o singura necunoscuta:
[tex]x+y-2z=129\\
x+\frac{14}{15}x+2\frac{196}{225}x=129\\[/tex]
Aducem la acelasi numitor, acesta fiind 225:
[tex]\frac{225}{225}x+\frac{14\cdot15}{15\cdot15}x-2\frac{196}{225}x=\frac{129\cdot225}{225}\Leftrightarrow \frac{225x+210x-392x}{225}\\
\\
=\frac{129\cdot225}{225}\Leftrightarrow \frac{43}{225}x=\frac{129\cdot225}{225}\\
43x=129\cdot225\\
x=\frac{129\cdot225}{43}=675\\
\\
y=\frac{14}{15}x=\frac{14}{15}\cdot675=630\\
\\
z=\frac{196}{255}x=\frac{196}{225}\cdot675=588[/tex]
