Question

Aflati numerele naturale nenule care impartite la 65 dau restulde 7 ori mai mare de cat catul

Answer 1

N : 65 = C rest ; rest = R = 7 × C

N = 65 × C + 7 × C

N = 72 × C

R = 7 × C < 65 => C = 1; 2; 3; 4; 5; 6; 7; 8; 9 .

N = 72 × 1 = 72
N = 72 × 2 = 144
N = 72 × 3 = 216
N = 72 × 4 = 288
N = 72 × 5 = 360
N = 72 × 6 = 432
N = 72 × 7 = 504
N = 72 × 8 = 576
N = 72 × 9 = 648
-------------------------

Verificam solutiile :
72 : 65 = 1 rest 7
144 : 65 = 2 rest 14
216 : 65 = 3 rest 21
288 : 65 = 4 rest 28
360 : 65 = 5 rest 35
432 : 65 = 6 rest 42
504 : 65 = 7 rest 49
576 : 65 = 8 rest 56
648 : 65 = 9 rest 63

Answer 2

d : 65= cat rest r , d ≠ 0 ⇒ catul ≠ 0

restul = 7 × cat < 65

catul = 1 ; 2; 3; 4; 5; 6 ; 7; 8; 9.

↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓

restul = 7; 14; 21; 28; 35; 42; 49; 56 63

Reconstitui impartirile pentru a determina valorile deimpartitului

d : 65 = 1 rest 7 ⇒ d = 1 × 65 + 7 = 65 + 7 = 72 → deimpartitul

d : 65 = 2 rest 14 ⇒ d = 2 × 65 + 14 = 130 + 14 = 144

d : 65 = 3 rest 21 ⇒ d = 3 × 65 + 21 = 195 + 21 = 216

d : 65 = 4 rest 28 ⇒ d = 4 × 65 + 28 = 260 + 28 = 288

d : 65 = 5 rest 35 ⇒ d = 5 × 65 + 35 = 325 + 35 = 360

d : 65 = 6 rest 42 ⇒ d = 6 × 65 + 42 = 390 + 42 = 432

d : 65 = 7 rest 49 ⇒ d = 7 × 65 + 49 = 455 + 49 = 504

d : 65 = 8 rest 56 ⇒ d = 8 × 65 + 56 = 520 + 56 = 576

d : 65 = 9 rest 63 ⇒ d = 9 × 65 + 63 = 585 + 63 = 648

Raspuns: 72; 144; 216; 288; 360; 432; 504; 576; 648 → numerele