Question

The sum of the digits of a two-digit number is 7. When the digits are reversed, then the original number is increaded by nine. Find the number.

Answer 1

Let the tens digti be t and the ones digit be o. Then the statements you have made translate to these equations:

(1) t + o = 7.
(2) 10o + t = 10t + o + 9

You now have two equations and two unknowns, so you can solve for both o and t. The easiest way to do so is probably to solve the first equation for t or o, then substitute the resulting expression into the second equation and solve for the remaining variable.

Answer 2

x+y=7
10y+x=10x+y+9

x=7-y, therefore

10y+7-y=70-10y+y+9
9y+7=79-9y
18y=72
y=4 and x=3