1. The problem statement, all variables and given/known data A number is made up of two digits. The sum of the digits is 11. If the digits are interchanged, the original number is increadsed by 9. Find the number. 2. Relevant equations I think this will definitely involve simultanous, quadratic or both of the equations. 3. The attempt at a solution Let the two digits number be xy. The sum of the digits is 11 -----> therefore x+y = 11 If the digits are interchanged, the original number is increased by 9 -----> forming equation from this last part is where am stuck. From my own point of view, "if the digits are interchanged", means, yx instead of xy as in the first equation. I also understand the original number which is increased by 9 as the sum x+y = 11. If 11 is increased by 9 when the two digit are interchanged, then the second equation should look like this yx = 11+9 then the two set of equation from the first and second sentence should look like this: x+y = 11 yx = 20 but this set of equations does not in any way help me, rather is making the problem more complex because the equation are not factorizable, each time I subtitute one variable into another such that quadratic equation is formed. I have used quadratic formular and completing the square method; I keep getting different values for x and y which is not true if you subtitute the values into the equations. Please I need help, maybe you can start by explaining what the second statement " if the digits are interchanged, the original number is increased by 9", mean and how to form equation with it. Thank you.