SOLUTION: The sum of a two digit number is 13. When 9 is subtracted from the original number, the resulting number is the reverse of the original number. What is the new number?

Question 178911: The sum of a two digit number is 13. When 9 is subtracted from the original number, the resulting number is the reverse of the original number. What is the new number?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a two digit number is 13. When 9 is subtracted from the original number, the resulting number is the reverse of the original number. What is the new number?
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Let the number be 10t+u
Equations:
t+u = 13
10t+u-9 = 10u+t
-------------------
Rearrange:
t + u = 13
9t - 9u = 9
--------------------
Simplify:
t + u = 13
t - u = 1
--------------
Add to solve for "t":
2t = 14
t = 7
---------
Since t+u = 13, u = 6
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The number is 76
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Cheers,
Stan H.

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