Question
The difference between a two-digit number and the number obtained by reversing its digits is 36. Find the number.
The difference between a two-digit number and the number obtained by reversing its digits is 36. Find the number.
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Koala Tutor
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Let the number be $10a+b$, where $a$ and $b$ are the tens and units digits of the number. Since the number is a two-digit, $a\ne 0$. We have \begin{align*}
10a+b-(10b+a)&=9(a-b)=36 \\
a-b&=4.
\end{align*} Adding $b$ to both sides gives $a=\boxed{4+b}$. Since $a$ and $b$ are non-negative integers less than 10, we can conclude that $a=4$ and $b=0$. Thus, the number is $\boxed{40}$.
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