Hi,         

Let x and (7-x) represent the original ten and units digits respectively

Question states:

Reversing its digits increases the number by 9

[10x + (7-x)] + 9 = 10(7 -x) + x

Solving for x

  9x + 16  = 70 - 9x

  18x = 54

    x = 3, the original ten's dgit, the original one's digit is 4.   (7-3)



CHECKING our Answer

   34 + 9 = 43 

Answer by lar(3)   (Show Source): You can put this solution on YOUR website!
 Let the digits of the number be x and y.

So the number is xy (note: this does not mean x times y).

x+y=7 and yx=xy+9

In order for yx to equal xy+9, x=y-1.

Now we have the two equations x+y=7 and x=y-1.

x+y=7 -> x=7-y

y-1=7-y

2y=8

y=4

Plug that into one of the original equations: x+4=7

x=3

The number is 34.

 

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