# The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 less than three times the original number. What is the original number? Thank you!

Apr 9, 2017

Number is $27$.

#### Explanation:

Let the unit digit be $x$ and tens digit be $y$

then $x + y = 9$ ........................(1)

and number is $x + 10 y$

On reversing the digits it will become $10 x + y$

As $10 x + y$ is $9$ less than three times $x + 10 y$, we have

$10 x + y = 3 \left(x + 10 y\right) - 9$

or $10 x + y = 3 x + 30 y - 9$

or $7 x - 29 y = - 9$ ........................(2)

Multiplying (1) by $29$ and adding to (2), we get

$36 x = 9 \times 29 - 9 = 9 \times 28$

or $x = \frac{9 \times 28}{36} = 7$

and hence $y = 9 - 7 = 2$

and number is $27$.