Question

Suma a doua numere este 47, iar suma rasturnatelor   lor este 173. Determinati cele doua numere

 

Answer 1

$\frac{}{ab}+ \frac{}{cd} =47$
$\frac{}{ba} + \frac{}{dc} =173$

deci
 10a+b+10c+d=47 => 10(a+c)+(b+d)=47 => b+d=47- 10(a+c)
10b+a+10d+c=173 => (a+c)+10(b+d)=173

=> a+c+10[47-10(a+c)]=173
a+c+470-100a-100c=173
297=99a+99c
a+c=3, dar a,d≠0, deci a=1 si c=2
b+d=47-30=17 , deci b=8 si d=9

Verificare:
18+29=47
81+92=173!

Answer 2

(10a+b) + (10c+d) = 47
 10(a+c)+(b+d)=47
y = 47- 10x
(10b+a) + (10d+c)  = 173
 (a+c)+10(b+d)=173, notam a+c = x si b+d = y
x + 10y = 173

 x+10(47-10x) = 173
x + 470-100x=173
297 = 99x
x = 3
a+c=3,
a=1 si c=2
 y = b+d =17 , b,d<=9
b=8 si d=9
Numerele sunt 18 si 29.