Question 444638
These are fun problems because they force you to reconsider what numbers mean.
Consider 15.  What does it mean?
Well, the 1 means 1*10.
And the 5 means 5*1.
So 15 means 1*10 + 5*1 = 10 + 5 = 15.
We can extend this notion to any sequence of letters, for example 'xy'.
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Do NOT get confused with 'xy' meaning x * y.
Here it would mean 10*x + 1*y.
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xy = the two-digit number, which 
x + y = 15
yx = xy + 9
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Looking back we realize that x and y have to be single digits.  And for them to = 15, they're either
9 + 6
8 + 7
7 + 8
6 + 9
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When the numbers are reversed, the difference is 9.
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Take 78, when turned around it is 87, which is 9 more.
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So xy = 78, which is the original number.
The sum 7+8 = 15.
When the order is reversed (i.e., 87) the value is 9 more than before the reversal.