<PRE><B>Question 1054978</B>
let x equal the first digit of the original number.
let y equal the second digit of the original number.


the original number is equal to 10x + y.


if you reverse the digits, then the number with the digits reversed is equal to 10y + x.


x + y = 14


10x + y = 10y + x - 18


simplify the second equation to get:


9x - 9y = -18


solve for x in the first equation to get x = 14 - y


replace x with 14 - y in the second equation to get:


9 * (14 - y) - 9y = -18


simplify to get 126 - 9y - 9y = -18


combine like terms to get 126 - 18y = -18


add 18 to both sides of the equation and add 18y to both sides of the equation to get:


126 + 18 = 18y


combine like terms to get 144 = 18y


divide both sides of the equation by 18 to get 144/18 = y


simplify to get 8 = y


since x + y = 14, then x must be equal to 6.


x + y = 14 becomes 14 = 14 which is true.


10x + y = 10y + x - 18 becomes 60 + 8 = 80 + 6 - 18 which becomes 68 = 86 - 18 which becomes 68 = 68 which is true.


the original number is 10x + y which is equal to 68.


the number with the digits reversed is equal to 10y + x which is equal to 86.



</PRE>