SOLUTION: the sum of digits of a two digit number is 13. the number obtained by interchanging the digits of given number exceeds the number by 23. find the number.

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Question 787014: the sum of digits of a two digit number is 13. the number obtained by interchanging the digits of given number exceeds the number by 23. find the number.
Found 3 solutions by CubeyThePenguin, ikleyn, josgarithmetic:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
number = AB ---> 10A + B

A + B = 13 ----> A = 13 - B
10B + A - (10A + B) = 23

Substitute the first equation into the second equation.

10B + A - (10A + B) = 23
11B - 9A = 23
11B - 9(13 - B) = 23
11B - 117 + 9B = 23
20B = 140
B = 7 ------> A = 6

original number = AB = 67

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

The problem formulated this way,  HAS  NO  solutions in integer  2-digit numbers.

The difference of any  2-digit number and its reversed number  CAN  NOT  be equal to  23.


So,  this problem is a  FAKE.



The solution presented by  @CubeyThePenguin,  is  WRONG.

For your safety,  IGNORE  it.

It contains  ELEMENTARY  ARITHMETIC  ERRORS.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
t, tens
u, units or ones
system%28t%2Bu=13%2C%2810u%2Bt%29-%2810t%2Bu%29=23%29

If you try to solve this system you would find 9u=70; meaning no whole number solutions, so meaningless problem description.