Michelle asked her father how old he is. “guess”, the father answered. “if you add the digits that make my age this year, you’ll get a number three times bigger than if you do it next year.” how old is the father?

Let the first digit that makes up the father's age be x and the second digit be y, then

x + y = 3(x + y + 1) = 3(x + y) + 3

=> 2(x + y) = -3

=> x + y = -3/2

But x + y cannot be negative, 

Thus, we have x + y = 3(x + 1 + y - 9) = 3(x + y - 8) = 3(x + y) - 24

=> 2(x + y) = 24
=> x + y = 12

Thus, the age of the father is 39.

39 years old. I will make an assumption that Michelle's father is younger than 99 years. Additionally, since we're looking at the sum of the digits becoming smaller the next year as compared to the current year, that would imply that the age ends in a 9. So the current age will be a number of the form: 10*x + 9 And the sum will be x + 9 And the age next year will be 10*x + 10 and the sum will be x + 1 Therefore we can create the following equation 3*(x+1) = x + 9 Now, solve for x 3*(x+1) = x + 9 3x+3 = x + 9 2x+3 = 9 2x = 6 x = 3 So the father is 10*3 + 9 = 39 years old.