Question

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

Answer 1

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

Answer 2

[tex]\widehat{ab}+\widehat{cd}=47\\ \widehat{ba}+\widehat{dc}=173 \\ 10(a+c)+(b+d)=47\\ 10(b+d)+(a+c)=173\\ 11(a+b+c+d)=220\Rightarrow a+b+c+d=20\\ \text{De asemenea:} \\ a+c=3\\ b+d=17\\ a=1,c=2,b=8,d=9\\ sau\\ c=1, a=2, b=9,d=8[/tex]
Se pot obtine solutii si interschimband valorile lui b si d.