Question

Suma a 3 nr naturale este 135.Impartind primele 2 nr. La al 3 obtinem caturile 12 si 31,iar resturile 1 si 2.Determinati cele trei nr.

Answer 1

$a + b + c = 135 \\ a \div c = 12(r = 1) \\ b \div c = 31(r = 2) \\ a = 12 \times c + 1 \\ b = 31 \times c + 2 \\ 12 \times c + 1 + 31 \times c + 2 + c = 135 \\ 44 \times c + 3 = 135 \\ 44 \times c = 132 \\ c = 3 \\ a = 12 \times 3 + 1 \\ a = 37 \\ b = 31 \times 3 + 2 \\ b = 95$