Question

1)Cate numere naturale de 3 cifre impartite la 23 dau restul 11? Aratati cum ati facut
2)fie a si b doua numere naturale nenule . Aflati restul impartirii lui x egal 15a+9b+20 la 3
3)Fie a b c numere naturale pentru care a+b egal 120 si b+c egal 230calculati:a)a+2b+c
b)5a+8b+3c

Answer 1

1) x:23=c rest11
x=23c+11⇒ x-11=23c+11-11
x-11=23c
x-1∈M23
M23={23,46,69,92,124.....}
x-11=92
x=92+11
x=103
103:23=4 rest 11
3) a+b=120⇒a=120-b
b+c=230⇒c=230-b
a)a+2b+c=120-b+2b+230-b=350
b)5a+8b+3c=
5(120-b)+8b+3(230-b)=
600-5b+8b+690-3b=1290