# A number is 3 more than 4 times the sum of its digits. If the digits are interchanged, the resulting number is 9 more than the given number. How do you find the Number?

Aug 31, 2016

$n = 23$

#### Explanation:

Keeping a two digit number, let

$n = 10 a + b$

then

{(10a+b=4(a+b)+3), (10b+a=10a+b+9):}

Solving for $a , b$ we obtain

$a = 2$ and $b = 3$ so the number is

$n = 23$