Question

Suma a trei nr naturale este 138.Impartind aceste nr la 5,la 6 si la 7 obtinem acelasi caturi si aceleasi resturi.Determinati numerele

Answer 1

a+b+c=138  si  a:5=x (rest y)   ⇒ a=5x+y

                         b:6=x (rest y)   ⇒ b=6x+y

                         c:7=x (rest y)   ⇒ c=7x+y

                                                         ⇅

                          a+b+c =  5x+y+6x+y+7x+y=138

                                               18x+3y = 138  | :3

                                                 6x + y = 46

                                                        ⇅

pt.x=0 => y=46 => a=5*0+46=46; b=6*0+46=46; c=7*0+46=46.

    x=1 => y=40 => a=5*1+40=45; b=6*1+40=46; c=7*1+40=47.

    x=2 => y=34 => a=5*2+34=44; b=6*2+34=46; c=7*2+34=48.

                                     s.a.m.d.