SOLUTION: In A Positive Number Of Two Digits, The Sum Of The Digits Is 15. If The Digits Are Interchanged, The Number Is Increased By 9. Find The Number.

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Question 1148319: In A Positive Number Of Two Digits, The Sum Of The Digits Is 15. If The Digits Are Interchanged, The Number Is Increased By 9. Find The Number.
Found 3 solutions by josgarithmetic, MathTherapy, Alan3354:
Answer by josgarithmetic(39630) About Me  (Show Source):
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Number 10t%2Bu

system%28t%2Bu=15%2Ct%2B10u-%2810t%2Bu%29=9%29

-9t%2B9u=9
-t%2Bu=1


Now simpler system is system%28u%2Bt=15%2Cu-t=1%29.


system%28u=8%2Ct=7%29


Number: 78

Answer by MathTherapy(10556) About Me  (Show Source):
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In A Positive Number Of Two Digits, The Sum Of The Digits Is 15. If The Digits Are Interchanged, The Number Is Increased By 9. Find The Number.
Only 2 DIGITS sum to 15. They are: 8 & 7, and 6 & 9. 

Now, which of these 2 digits, when interchanged, DIFFER by 9? I do believe that you can see this, and therefore able o solve this "mystery!"

Answer by Alan3354(69443) About Me  (Show Source):
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Swapping the digits of a 2 digit number changes the number by 9 times the difference between the digits.