<PRE><B>Question 1199873</B>
&lt;br&gt;
If a formal algebraic solution is not required, you can use a shortcut to solve the problem.&lt;br&gt;
When a 2-digit number has its digits reversed and the two numbers are compared, the difference is 9 times the difference between the digits.&lt;br&gt;
In this problem, the difference between the two numbers is 45, so the difference between the two digits is 5.&lt;br&gt;
Now we know the sum of the digits is 11 and their difference is 5; quick reasoning and mental arithmetic tells us the two digits are 8 and 3.&lt;br&gt;
Then, since the original number is greater, it is 83.&lt;br&gt;
ANSWER: 83&lt;br&gt;
It is easy to prove algebraically that the difference of the two numbers is 9 times the difference of the digits.&lt;br&gt;
Let the original number have tens digit a and units digit b; the value of the number is 10a+b.&lt;br&gt;
The number with the digits reversed has the value 10b+a.&lt;br&gt;
The difference between the two numbers is&lt;br&gt;
(10a+b)-(10b+a) = 9a-9b = 9(a-b)&lt;br&gt;
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