SOLUTION: The sum of the digits is 9. If the digits are reversed, the new number is 45 more than the original number. Find the two digit number.

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Question 26725: The sum of the digits is 9. If the digits are reversed, the new number is 45 more than the original number. Find the two digit number.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
we could probably do this by looking:

Easy possibles are
18 and 81
27 and 72
36 and 63
45 and 54

Looking, 27+45 is 72 so 27 is your answer.


OK, mathematically...

Let tens be x and units be y --> x+y = 9
Also, (10y+x) - (10x+y) = 45
10y+x-10x-y = 45
9y-9x = 45

we have
y+x = 9
9y-9x = 45

multiply first by 9 and we get
9y+9x = 81
9y-9x = 45

Now subtract, leaving 18x = 36. So x = 2. Therefore, from x+y=9, y must be 7.

jon.