What is the smallest positive 2-digit whole number divisible by 3 and such…

Key insight: the smallest two-digit number with digits summing to 9 has the smallest possible tens digit (which is 1).

• Step 1: Let the tens digit be x and the units digit be y, with x + y = 9. For a two-digit number x must be at least 1, so the smallest possible tens digit is 1.

• Step 2: With x = 1 and x + y = 9 we get y = 8, so the number is 18.

• Step 3: A number is divisible by 3 exactly when the sum of its digits is divisible by 3. Since 1 + 8 = 9 and 9 is divisible by 3, 18 is divisible by 3.

• Conclusion: The smallest positive two-digit whole number whose digits sum to 9 and that is divisible by 3 is 18.