# Question #f0641

Mar 10, 2017

Original number: $\textcolor{g r e e n}{45}$

#### Explanation:

If $a$ is the tens digit and $b$ is the units digit.
The original number is $10 a + b$
and the number with the digits reversed is $10 b + a$

Since the number with the digits reversed is $9$ more than the original number:
$\left(10 b + a\right) - \left(10 a + b\right) = 9$

$\rightarrow 9 b - 9 a = 9$

$\rightarrow b - a = 1$

$\rightarrow a = b - 1$

We are also told that
$a + b = 9 \rightarrow a = 9 - b$

So
$b - 1 = 9 - b$

$\rightarrow 2 b = 10$

$\rightarrow b = 5$

and since $a = 9 - b$
$\rightarrow a = 4$