Question 1636
Let  t = tens digit
     u = units digit


The value of the original number is ten times the tens digit plus the units digit.  That is, 10 t + u.


If the digits are reversed, then u becomes the tens digit, and t becomes the units digit, and the value of the number is 10u + t.


Since there are two variables, you need to find two equations.


"The sum of the digits is seven."
t + u = 7


"If digits are reversed, the new number is nine less than the original."
10u + t = 10t + u - 9.  


Simplify this equation by subtracting 10t and u from each side of the equation.
10u + t - 10t - u = -9   


Simplify this equation and divide both sides of the resulting equation by 9:
-9t + 9u = -9   
-t + u = -1


Now you have two equations that you can add together:
t + u = 7
-t + u = -1


2u = 6
u = 3


Since the sum of the digits is 7, that makes t = 4.
The original number is 43, and the new number, with digits reversed, is 34.  


Check:  When the digits are reversed, the new number is indeed 9 less than the original number.


R^2 at SCC