Fie a și b cele două numere, b > a .
[tex]\it b - a = 15 \Rightarrow b = a+15\ \ \ \ \ (1)\\ \\ \\ \dfrac{a}{b}=\dfrac{2}{3} \Rightarrow b=\dfrac{3a}{2}\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \dfrac{3a}{2}=a+15\bigg|_{\cdot2} \Rightarrow 3a=2a+30\bigg|_{-2a} \Rightarrow a=30\ \ \ \ \ \ (3)\\ \\ \\ (1),\ (3) \Rightarrow b=30+15 \Rightarrow b=45.[/tex]
