Question

Suma a douã numere este 47, iar suma rãsturnatelor este 173. Determinati cele doua numere.

Answer 1

Trebuie sa fie de 2 cifre
ab + cd = 47
ba + dc = 173

10a + b + 10c + d = 47
10b + a + 10d + c = 173

10a + b + 10c + d + 10b + a + 10d + c = 47+173
11a + 11b + 11c + 11d = 220
11(a+b+c+d) = 220
a+b+c+d = 20

10a + b + 10c + d - a - b - c - d = 47-20
9a + 9c = 27
9(a+c) = 27
a+c = 3
$(a,c)\in\{(1,2),(2,1)\}$

b+d = 17
$(b,d)\in\{(8,9),(9,8)\}$

$(a,b,c,d)\in\{(1,8,2,9),(1,9,2,8),(2,8,1,9),(2,9,1,8)\}$
$(\bar{ab},~\bar{cd})\in\{(18,29),(19,28),(28,19),(29,18)\}$