Question 1000123
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<U>Answer</U>. 56.


<U>Solution</U>


Let &nbsp;<B>a</B>&nbsp; and &nbsp;<B>b</B>&nbsp; be the digits of your number &nbsp;n, &nbsp;so that &nbsp;n = 10a + b.


The number after interchanging digits is &nbsp;10b + a.


Thus you have the system of two equations for the unknowns &nbsp;<B>a</B>&nbsp; and &nbsp;<B>b</B>:


{{{system(a+b = 11,

(10b +a) - (10a + b) = 9)}}}.


Now, &nbsp;simplify it:


{{{system (a+b= 11,

9b - 9a = 9)}}}. 


Simplify it one more time:


{{{system (a+b= 11,

b - a = 1)}}}. 


Solve it.


The solution is &nbsp;&nbsp;b=6, &nbsp;a=5.


Hence, &nbsp;the number is &nbsp;10a + b = 10*5+6 = 56.