# When you reverse the digits in a certain two-digit number you decrease its value by 18. What is the number if the sum of its digits is 12?

Feb 21, 2017

$= 75$

#### Explanation:

We can also write

$\left(10 x + y\right) - \left(10 y + x\right) = 18$ ---------------EQ(1)

And also

$x + y = 12$ ------------------------------EQ(2)

By simpifying EQ(1) we get

$9 x - 9 y = 18$

or

$9 \left(x - y\right) = 18$

or

$x - y = \frac{18}{9}$

or

$x - y = 2$--------------------------------------EQ(3)

By adding up EQ(2) and EQ(3) we get

$x + y + x - y = 14$

or

$2 x = 14$

or

$x = \frac{14}{2}$

or

$x = 7$

By plugging the value of $x$ in the EQ(3) we get

$7 - y = 2$

or

$y = 7 - 2$

or

$y = 5$

Therefore the Number is $10 x + y = 75$