Question

Tìm các chữ số a,b,c khác nhau sao cho:

\(\overline{a,bc}\) : (a+b+c)=0,25

Answer 1

Ta biến đổi:

\(\overline{abc}\) \(=\) \(25\left(a+b+c\right)\Rightarrow\overline{abc}⋮25\)

\(\Rightarrow\overline{bc}\in\left\{25;50;75\right\}\)

Nếu \(\overline{bc}=25\) thì \(\overline{a25}=25\left(a+7\right)\)

\(\Rightarrow100a+25=25a+175\)

\(\Rightarrow75a=150\)

\(\Rightarrow a=2\) (loại vì a = b)

Nếu \(\overline{bc}=50\) thì \(\overline{a50}=25\left(a+5\right)\)

\(\Rightarrow100a+50=25a+125\)

\(\Rightarrow75a=75\Rightarrow a=1\)

Nếu \(\overline{bc}=75\) thì \(\overline{a75}=25\left(a+12\right)\)

\(\Rightarrow100a+75=25a+300\)

\(\Rightarrow75a=225\Rightarrow a=3\)

Vậy:\(\left[{}\begin{matrix}1,50\div\left(1+5+0\right)=0,25\\3,75\div\left(3+7+0\right)=0,25\end{matrix}\right.\)