# The sum of the in a two digit number is 17. lf the digits are reversed, the new digits number will be 9 less than the original number. What is the original number?

##### 1 Answer
Oct 4, 2016

The number is $98$

#### Explanation:

Let the number be $10 x + y$

So we can write

$x + y = 17$------------------------------Eq $1$

Reverse of the number will be $10 y + x$

So we can write

$\left(10 x + y\right) - \left(10 y + x\right) = 9$

or

$9 x - 9 y = 9$

or

$9 \left(x - y\right) = 9$

or

$x - y = \frac{9}{9}$

or

$x - y = 1$-------------------Eq $2$

Adding up the Eq $1$ and Eq $2$

we get

$x + y + x - y = 17 + 1$

or

$2 x + 0 = 18$

or

$2 x = 18$

or

$x = \frac{18}{2}$

or

$x = 9$

By plugging the value $x = 9$ in the $x + y = 17$

We get

$9 + y = 17$

or

$y = 17 - 9$

or

$y = 8$

Therefore the number is $98$