Question 40016
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.