Question

0(1x)+0,(2x)+0,(3x)+0,(4x)=1,(25)

Answer 1

[tex]\overline{0,(1x)}+\overline{0,(2x)}+\overline{0,(3x)}+\overline{0,(4x)}=1,(25)\\ \dfrac{\overline{1x}}{99}+\dfrac{\overline{2x}}{99}+\dfrac{\overline{3x}}{99}+\dfrac{\overline{4x}}{99}=1\dfrac{25}{99}\\ \\ \dfrac{10+x}{99}+\dfrac{20+x}{99}+\dfrac{30+x}{99}+\dfrac{40+x}{99}=\dfrac{99+25}{99}|\cdot 99\\ 10+x+20+x+30+x+40+x=124\\ 100+4x=124\\ 4x=24\\ \boxed{x=6}[/tex]