SOLUTION: the ones digit of a 2 digit number is 2 greater than the tens digit, if the original number is subtracted from its interchanged form the difference is 18,find the original number

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Question 630266: the ones digit of a 2 digit number is 2 greater than the tens digit, if the original number is subtracted from its interchanged form the difference is 18,find the original number
Answer by dfrazzetto(283) About Me  (Show Source):
You can put this solution on YOUR website!
digits: xy
x is the tens digit
number represented : 10x + y
y = 2 + x
the tens digit must be smaller than the ones digit to give a positive difference:
yx - xy
10y + x - (10x + y) = 18
10(2 + x) + x - 10x - 2 - x = 18
20 + 10x + x - 10x -2 -x = 18
18=18, cannot be solved explicitly algebraically; must use iteration
13
31 - 13 = 18
24
42 - 24 = 18
35
53 - 35 = 18
46
64 - 46 = 18
Works for ANY 2 digit number such that XY, Y = X+2