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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
Plug that into one of the original equations: x+4=7
The number is 34.