Question

 URGENT!Determinati nr abc (cu bara de asupra)astfel incat 15b +20c=16a(cu bara de asupra)

Answer 1

$15b+20c= \overline{16a} \Leftrightarrow 5(3b+4c)= \overline{16a} \Rightarrow \overline{16a} ~ \vdots ~5 ,~dar~a \neq 0 \Rightarrow a=5. \\ \\ Avem~5(3b+4c)=165 \Leftrightarrow \boxed{3b+4c=33} \Leftrightarrow 4c=33-3b \Leftrightarrow \\ \\ \Leftrightarrow 4c=3(11-b) \Rightarrow 3 ~|~4c \Rightarrow ~3~|~c,~dar~c~este~cifra~\Rightarrow c \in \{0,3,6,9 \}. \\ \\ c=0 \Rightarrow 3b=33 \Rightarrow b=11,~nu~convine. \\ \\ c=3 \Rightarrow 3b+12=33 \Rightarrow 3b=21 \Rightarrow b=7.$

$c=6 \Rightarrow 3b+24=33 \Rightarrow 3b=9 \Rightarrow b=3. \\ \\ c=9 \Rightarrow 3b+36=33,~nu~convine. \\ \\ \underline{Solutie}:~ \overline{abc} \in \{536;~573 \}$