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

Question 40016: 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
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
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.

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