Question

aflati cifrele a,b,c stiind ca :abc+bc+c=687

Answer 1

$Voi~aseza~numerele~unele~sub~altele~(adunare~etajata). \\ \\ ABC+ \\ ~~~BC \\ ~~~~~C \\ ---- \\ 6~8~7 \\ \\ Suma~C+C+C~are~ultima~cifra~egala~cu~7~\Rightarrow~C=9. \\ \\ AB9+ \\ ~~~B9 \\ ~~~~~9 \\ ---- \\ 6~8~7$

$Suma~B+B+2~are~ultima~cifra~egala~cu~8 \Rightarrow B=3~sau~B=8. \\ \\ Cazul~I:~B=3 .\\ \\ \\ A39 +\\ ~~~39 \\ ~~~~~9 \\ ---- \\ 6~87 \\ \\ Rezulta~A=6.$

$Cazul~II:~B=8 \\ \\ A89+ \\ ~~~89 \\ ~~~~~9 \\ ---- \\ 6~87 \\ Rezulta~A=5. \\ \\ Solutie:~A=6,~B=3~si~C=9; \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~si~ \\~~~~~~~~~~~~~~ A=5,~B=8~si~C=9.$