# The sum of the digit's of a two digit number is 9. The number is 12 times the ten's digit. How do you find the number?

May 18, 2018

36

#### Explanation:

"the number is 12 times the ten's digit" so the number must be a multiple of 12

listing out 2-digit multiples of 12 gives us

12
24
36
48
60
72
84
96

there is only one number where the digits add up to 9 AND the entire number is 12 times the tens digit, and that's $36$

$36 = 12 \cdot 3$
$3 + 6 = 9$