Question

Suma a trei numere naturale este 435.Impartind aceste numere 6,7,8 obtinem aceleasi caturi si aceleasi resturi.Determinati cele trei numere.

Answer 1

x+y+z=435

x:6=c, rest r => x=6c+r => r<6

y:7=c, rest r=>y=7c+r

z:8=c, rest r=> z=8c+r =>

x+y+z=6c+7c+8c+3r

21c+3r=435

7c+r=145 si r<6

=> r=5 si c=20

x=6•20+5=125

y=7•20+5=145

z=8•20+5=165

x=125; y=145; z=165

x+y+z=125+145+165=435  (A)