Question 1011629
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Let &nbsp;<B>a</B>&nbsp; and &nbsp;<B>b</B> are the digits of your number &nbsp;n, &nbsp;so that &nbsp;n = 10a + b.


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


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


{{{system(a+b = 9,

(10b +a) - (10a + b) = 45)}}}.


Now, &nbsp;simplify it:


{{{system (a+b= 9,

9b - 9a = 45)}}}. 


Simplify it one more time:


{{{system (a+b= 9,

b - a = 5)}}}. 


Solve it.


The solution is &nbsp;&nbsp;b=7, &nbsp;a=2.


Hence, &nbsp;the number is &nbsp;10a + b = 10*2+7 = 27.


<B>Answer</B>. &nbsp;27. 


For more problems of this type see the lesson <A HREF=http://www.algebra.com/algebra/homework/word/misc/Word-problems-on-interchanging-digits-of-numbers.lesson>Word problems on interchanging digits of numbers</A> in this site.