Question

aflati cifrele a si b stiind ca (a si b naturale)
3 x ab + ba =114

Answer 1

$a,b \neq 0 \\ 3*\overline{ab}+ \overline{ba}=114 \Leftrightarrow 3(10a+b)+10b+a=114 \Leftrightarrow \\ \Leftrightarrow 30a+3b+10b+a=114 \Leftrightarrow 31a+13b=114. \\ 31a \ \textgreater \ 0~si~13b\ \textgreater \ 0 \Rightarrow 31a\ \textless \ 114 \Rightarrow a \in \{1;2;3\}. \\ a=1 \Rightarrow 31+13b=114 \Leftrightarrow 13b=83,~nu~convine. \\ a=2 \Rightarrow 62+13b=114 \Leftrightarrow 13b=52 \Rightarrow b=4. \\ a=3 \Rightarrow 93+13b=114 \Leftrightarrow 13b=21, ~nu ~convine. \\ \\ Solutie:~\boxed{\overline{ab}=24}.$