SOLUTION: The sum of the digets of a two digit number is 10. if the digets were reversed, the new number would be 54 less than the original number. find the original number. thanx

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Well, from just thinking about it:

19 and 91 --> difference is 72
28 and 82 --> difference is 54
37 and 73 --> difference is 46
46 and 64 --> difference is 18

so you have your answer there: 28 and 82

OK, algebraically:

Let the number be written as xy where x+y=10

xy means the number is (10x+y) like 28 is (10*2 + 8)
and yx is the reversed version: (10y+x)

and we are told that new number = old number - 54
--> 10y+x = 10x+y - 54
9y-9x = -54
or 9x-9y = 54 (just swapping all the signs over --> like moving the lefthand terms to the right hand side and vice versa)

So, we have:
9x-9y = 54
x+y = 10

9x-9y = 54
9x+9y = 90

Now, add the 2 equations together:
18x = 144
x = 144/18
x = 8

and so y must be 2.

So answer is: original number, xy, is 82

jon.