Notm cele două numere cu a și b.
[tex]\it b\ \ |\rule{20}{0,7}|\\ \\ a\ |\rule{20}{0,7}|\ \ \ +238\\ \\ a\ \ |\rule{20}{0,7}||\rule{20}{0,7}||\rule{20}{0,7}||\rule{20}{0,7}||\rule{20}{0,7}|+b/4\\ \\ a-b\ \ \ \ |\rule{20}{0,7}||\rule{20}{0,7}||\rule{20}{0,7}||\rule{20}{0,7}|+b/4\\ \\ 4b+\dfrac{b}{4}=238 \Rightarrow 4\cdot4\dfrac{b}{4}+\dfrac{b}{4}=238 \Rightarrow 16\dfrac{b}{4}+\dfrac{b}{4}=238 \Rightarrow \\ \\ \\ \Rightarrow 17\cdot\dfrac{b}{4}=238\Rightarrow \dfrac{b}{4}=238:14 \Rightarrow \dfrac{b}{4}=14 \Rightarrow b=4\cdot14=56[/tex]
[tex]\it a=56+238 \Rightarrow a=294[/tex]
Sau:
[tex]\it a-b=238 \Rightarrow a=238+b\ \ \ \ \ (1)\\ \\ a:b=5\ rest\ \dfrac{b}{4} \Rightarrow a=5b+\dfrac{b}{4} \Rightarrow a=\dfrac{21b}{4}\ \ \ \ \ (2) \\ \\ \\ (1),(2) \Rightarrow \dfrac{21b}{4}=238+b|_{\cdot4} \Rightarrow 21b=4\cdot238+4b|_{-4b} \Rightarrow \\ \\ \Rightarrow 17b=4\cdot238|_{:7} \Rightarrow b=4\cdot14 \Rightarrow b=56\ \ \ \ (3)\\ \\ (1),\ (3) \Rightarrow a=238+56 \Rightarrow a=294[/tex]
Numerele cerute sunt 294 și 56.
