# The sum of the digits of a two digit number is 9. If the digits are reversed, the new number if 63 greater than the original number. How do you find the original number.?

Nov 8, 2015

18

#### Explanation:

Let $x$ be the ones digit
$\implies$ The tens digit is $9 - x$

$10 \left(9 - x\right) + x + 63 = 10 x + \left(9 - x\right)$

$\implies 90 - 10 x + x + 63 = 10 x + 9 - x$

$\implies 153 - 9 x = 9 x + 9$

$\implies 153 - 9 = 18 x$

$\implies 144 = 18 x$
$\implies x = 8$

$\implies 9 - x = 9 - 8 = 1$

Therefore, the number we are looking for is

$10 \left(1\right) + 8 = 18$