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Question 369029: unit digit of 2 digit number is 6 more than it's ten's digit.if reverse the digit we find 54 more than original number.find the original number.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Let  represent the 10s digit of the original number. Let  represent the units digit of the original number. The original number is then  , the number with the digits reversed is  , and the digits are related by  .
If reversing the digits increases the number by 54, then we can say:
Since we know that , we can substitute:
\ =\ -54)
Which results in the triviality:
Ordinarily when solving a system of equations such a result would indicate that the system was consistent and dependent, which is to say that the solution set has an infinite number of elements. However, in this problem our variables are restricted to the set of single digit positive integers, namely 
The smallest value can assume is 1 which implies that would be 7 and the original number would be 17. could also be 2,  8, and the original number 28, or could be 3, 9, and the original number 39. This exhausts the possibilities.
Verification that each of the three results above fit the parameters given in the problem is left as an exercise for the student.
John
My calculator said it, I believe it, that settles it
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