SOLUTION: the sum of two digit number and the number obtained by interchanging its digits is 99. find the number

Question 1096584: the sum of two digit number and the number obtained by interchanging its digits is 99. find the number
Found 3 solutions by greenestamps, ikleyn, MathTherapy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Are you supposed to use algebra to solve this? That's overkill. The problem is easily solved using logical analysis.

You are adding the two 2-digit numbers AB and BA, and the sum is 99. It should be clear that the two digits A and B can be any two non-zero digits with a sum of 9. So the number could be any one of
18 27 36 45 54 63 72 81
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Let a and b be the digits of your number n, so that n = 10a + b. The number after reversing digits is 10b + a. Then from the condition you have the system of two equations for the unknowns a and b: . Now, simplify it: . Simplify it one more time: . So, you have, actually, only ONE equation for the digits and do not have any additional info. Therefore, the answer is not unique. All the numbers 18, 27, 36, 45, 54, 63, 72, 81 are the solutions.

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On problems for digits reversing see the lesson
    - Word problems on reversing digits of numbers
in this site.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

the sum of two digit number and the number obtained by interchanging its digits is 99. find the number

Let the tens and units digits be T and U, respectively
Then the number is 10T + U, and the reversed number is 10U + T
We then get: 10T + U + 10U + T = 99
11T + 11U = 99
11(T + U) = 11(9)
T + U = 9
Therefore, any 2 digits that sum to 9 will satisfy. It's NOT unique as there're more than 1 answers.
In other words, the digits can be: 1 and 8, or the number 18, the reverse being 81
2 and 7, or the number 27, the reverse being 72
3 and 6, or the number 36, the reverse being 63
4 and 5, or the number 45, the reverse being 54
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