Răspuns :
bc = 4% x(100a +bc) /x100 ( 4% = 0,04)
100bc = 400a +4bc
100bc - 4bc = 400a
96bc = 400a / : 16
6bc = 25a
c = se termina in 0 = > 6bc , 25a = numere pare
a = un numar par, divizibil cu 3
avem = > a = 6 = > b=2 = > c =5
reese , ca a + b + c = 6 + 2 + 5 = 13
100bc = 400a +4bc
100bc - 4bc = 400a
96bc = 400a / : 16
6bc = 25a
c = se termina in 0 = > 6bc , 25a = numere pare
a = un numar par, divizibil cu 3
avem = > a = 6 = > b=2 = > c =5
reese , ca a + b + c = 6 + 2 + 5 = 13
[tex]\it \overline{bc} = \dfrac{4}{100}\cdot \overline{abc} \Rightarrow 100\cdot \overline{bc} =4\cdot \overline{abc}|_{:4} \Rightarrow 25\cdot\overline{bc} =\overline{abc} \Rightarrow \\\;\\ \\\;\\ \Rightarrow 25\overline{bc} = 100a +\overline{bc}|_{-\overline{bc}} \Rightarrow 24\overline{bc} = 100a|_{:4} \Rightarrow 6\overline{bc} = 25a \Rightarrow [/tex]
[tex]\it \Rightarrow 6\cdot\overline{bc} = a\cdot25[/tex]
Deoarece (6, 25) =1, vom avea:
[tex]\it \begin{cases} \it a=6 \\\;\\ \overline{bc} = 25\Rightarrow b=2,\ \ c = 5 \end{cases} \\\;\\ \\\;\\ a+b+c = 6+2+5 = 13[/tex]