20.
a + b + c= 243
a : c = 12 rest 7⇒ a = 12c + 7
b: c = 5 rest 2 ⇒ b = 5c + 2
(12c + 7 ) + (5c + 2) + c= 243⇒ 18c + 9=243⇒ 18 c = 234⇒ c = 234:18
c = 13 dar b =5c + 2 = 5 × 13 + 2= 65 + 2 = 67 deci
b = 67
a = 12c+7 = 12× 13 + 7= 156 + 7= 163
c = 63
21.
Aplicam Teorema impartirii cu rest
restul r ∈ {0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36}
37 × 1 + 1 = 38 38 : 37 = 1 rest 1
37 × 2 + 2 = 76 76 : 37 = 2 rest 2
37 × 3 + 3 = 114 114 : 37 = 3 rest 3
..................................................
37 × 35 + 35 = 1330 1330 : 37 = 35 rest 35
37 × 36 + 36 = 1368 1368 : 37 = 36 rest 36
deci sunt in total 37 de valori
22.
Numerele care impartite la 8 dau catul 13 sunt: 104, 105, 106, 107, 108, 109, 110 si 111.
a: 8 = 13⇒ a = 13× 8 =104
Suma lor este 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 = 860
23.
a-b=348
a = 2b + 65⇒
2b + 65 - b = 348⇒b + 65 = 348⇒ b = 348 - 65
b = 283
a = 283×2 + 65⇒ a = 631
