LET xy be the whole number with x and y the TWO digits that make up the number.

The number is divisible by 3 may be written as follows 

10 x + y = 3 k 

The sum of x and y is equal to 9. 

x + y = 9 

Solve the above EQUATION for y 

y = 9 - x Substitute y = 9 - x in the equation 10 x + y = 3 k to obtain. 

10 x + 9 - x = 3 k 

Solve for x 

x = (k - 3) / 3 

x is a positive integer smaller than 10 

Let k = 1, 2, 3, ... and select the first value that gives x as an integer.

k = 6 gives x = 1 

Find y USING the equation y = 9 - x = 8 

The number we are looking for is 18.

It is divisible by 3 and the sum of its digits is equal to 9 and it is the smallest and positive whole number with such properties.

Let xy be the whole number with x and y the two digits that make up the number.

The number is divisible by 3 may be written as follows 

10 x + y = 3 k 

The sum of x and y is equal to 9. 

x + y = 9 

Solve the above equation for y 

y = 9 - x Substitute y = 9 - x in the equation 10 x + y = 3 k to obtain. 

10 x + 9 - x = 3 k 

Solve for x 

x = (k - 3) / 3 

x is a positive integer smaller than 10 

Let k = 1, 2, 3, ... and select the first value that gives x as an integer.

k = 6 gives x = 1 

Find y using the equation y = 9 - x = 8 

The number we are looking for is 18.

It is divisible by 3 and the sum of its digits is equal to 9 and it is the smallest and positive whole number with such properties.