# Number is 5 less than 9 times the sum of the digits. How do you find the number?

##### 1 Answer

#### Answer:

#### Explanation:

Suppose that the number is

The sum of its digits is

Then, according to the problem statement,

Simplify to get

Recall that all variables are integers between

This is because the maximum value

#8a# can be is#8*9=72# , while the minimum value of#91c,991d,9991e,ldots# where#c,d,e,ldots≠0# is#91,991,9991,ldots#

As most of the terms evaluate to zero, we have

Since the maximum possible value for

So only