Summer Clouds moderators
06/11/2017 at 15:33-
Tell the number to find is \(\overline{ab0}\)
\(\Rightarrow\left\{{}\begin{matrix}a+b=12\\\overline{ba0}-\overline{ab0}=540\end{matrix}\right.;a< b\)because \(\overline{ba0}>\overline{ab0}\)
=> \(\left(100b+10a\right)-\left(100a+10b\right)=540\)
=> 100b + 10a - 100a - 10b = 540
=> 90b - 90a = 540
\(\Rightarrow90\left(b-a\right)=540\)
\(\Rightarrow b-a=6\)
\(So-\left\{{}\begin{matrix}a=\dfrac{12-6}{2}=3\\b=\dfrac{12+6}{2}=9\end{matrix}\right.\)
So the original number is 390
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