Question 1207727
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Here is an important note regarding the work you show in trying to set up the problem.<br>
The statement of the problem says "if 9 is subtracted from the number..."<br>
You need to pay attention to what the whole phrase says, and not just write math symbols representing the given words.<br>
"9" is SUBTRACTED FROM the number.  The mathematical expression representing those words has to show that the 9 is being subtracted:
(the number) minus (9) --> (10a+b)-9  --  not "9-(10a+b)", as you show in your work.<br>
Then a formal algebraic solution can be obtained from this correct expression as shown in the response from the other tutor.<br>
This is a common type of problem on competitive math contest exams.  If a formal algebraic solution is not needed, note that when the digits of a 2-digit number are reversed, the difference between the original number and the new number is always 9 times the difference between the two digits.<br>
In this problem, the sum of the two digits is 5, and the difference between the two numbers is 9 = 9*1, so the difference between the two digits is 1.<br>
So the sum of the two digits is 5 and the difference between the two digits is 1; that means the two digits are 2 and 3.<br>
Finally, since 9 was subtracted from the original number to get the new number, the original number is larger than the new number; that makes the original number 32 and the new number 23.<br>
ANSWER: 32<br>