ab + cd = 47 → suma a doua numere
ba + dc = 173 → suma rasturnatelor celor doua numere
_______________________ → adun sumele
10 a + b + 10 c + d + 10 b + a + 10 d + c = 47 + 173
11 a + 11 b + 11 c + 11 d = 220
11 ( a + b + c + d ) = 220
a + b + c + d = 220 : 11
a + b + c + d = 20 → suma cifrelor celor doua numere si a rasturnatelor acestora
______________________
( ba + dc ) - ( ab + cd ) = 173 - 47
10 b + a + 10 d + c - 10 a - b - 10 c - d = 126
9 b + 9 d - 9 a - 9 c = 126
9 ( b + d - a - c ) = 126
b + d - a - c = 126 : 9
b + d - a - c = 14
_____________
( a + b + c + d ) - ( b + d - a - c ) = 20 - 14
a + b + c + d - b - d + a + c = 20 - 14
2 a + 2 c = 6
2 ( a + c ) = 6
a + c = 6 : 2
a + c = 3 ⇒ a + b + c + d = 20 ⇒ b + d = 17
a,b, c, d ≠ 0
Solutii: ( ab; cd) = ( 18; 29); ( 28; 19)
Verific:
18 + 29 = 29 + 18 = 47 → suma celor doua numere
81 + 92 = 92 + 81 = 173 → suma rasturnatelor celor doua numere
