The sum of two digits of a number is 15. if 9 is added to the number, the digit is reversed. The numbers are?

This problem is a classic example of a two-variable algebraic problem. Here are the steps to solve it:

1. Let's denote the tens digit as "x" and the units digit as "y". According to the problem, the sum of the two digits is 15. So, we can write the first equation as: x + y = 15.

2. The second condition in the problem states that if 9 is added to the number, the digits are reversed. This means that the original number (which is 10x + y) plus 9 equals the reversed number (which is 10y + x). So, we can write the second equation as: 10x + y + 9 = 10y + x.

3. Now we have a system of two equations, and we can solve it. First, simplify the second equation to 9x - 9y = -9.

4. Divide the entire equation by 9 to simplify it further: x - y = -1.

5. Now you have a system of two equations: x + y = 15 and x - y = -1. You can solve this system by adding the two equations together to eliminate "y". This gives: 2x = 14, so x = 7.

6. Substitute x = 7 into the first equation to find the value of y: 7 + y = 15, so y = 8.

7. Therefore, the two-digit number is 78.