Question

Aflati cel mai mic numar natural de forma abc,stind ca abc:bc=3 rest 36

Answer 1

$\it \overline{abc}:\overline{bc}=3\ rest\ 36\Rightarrow \begin{cases}\it \overline{abc}=3\cdot\overline{bc}+36\ \ \ (1)\\ \\ \it\overline{bc}>36\ \ \ \ (2)\end{cases}\\ \\ \\ (1)\Rightarrow 100a+\overline{bc}=3\cdot\overline{bc}+36 \Rightarrow 100a=2\cdot\overline{bc}+36|_{:2}\Rightarrow \\ \\ \Rightarrow50a=\overline{bc}+18\ \ \ \ (3)$

$\it (2),\ (3) \Rightarrow a=2,\ \ \overline{bc} =82\\ \\ Deci,\ \overline{abc}=282$