A two-digit number has digits whose sum is 12 and whose difference is 6. What is the number?

Explanation

Let the digits be a and b, forming the number 10a + b. Given that a + b = 12. The difference between the digits is 6, so either a - b = 6 or b - a = 6. If a - b = 6, adding this to the sum equation gives 2a = 18, so a = 9 and b = 3, making the number 93. If b - a = 6, then 2b = 18, so b = 9 and a = 3, making the number 39. Therefore, the number can be either 93 or 39.