Question 1166205
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I didn't look closely at the solution by the other tutor.  There are many ways to solve the problem using formal algebra; that solution shows one of them.<br>
If a formal algebraic solution is not required, a bit of logical reasoning and some simple mental arithmetic will find the answer quickly.<br>
Logical analysis should easily show that, since switching the hundreds and tens digit reduces the number by 90, the hundreds digit is 1 more than the tens digit.<br>
Then the requirement that the sum of the digits be 11 leaves only a very few possibilities for the number:
218
326
434
542
650<br>
In only one of those numbers is the other requirement satisfied -- that the difference between the first and third digits is one less than the middle digit: 542.<br>
ANSWER: 542<br>