SOLUTION: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. what are the two equations?

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Question 381751: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. what are the two equations?
Found 2 solutions by ewatrrr, lar:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


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) About Me  (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.