SOLUTION: a number is made of two digit. the sum of the digit is 11. if the digit is interchange the original number is increased by 9. find the numbers.

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Question 1000123: a number is made of two digit. the sum of the digit is 11. if the digit is interchange the original number is increased by 9. find the numbers.
Answer by ikleyn(52946) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer. 56.

Solution

Let  a  and  b  be the digits of your number  n,  so that  n = 10a + b.

The number after interchanging digits is  10b + a.

Thus you have the system of two equations for the unknowns  a  and  b:

system%28a%2Bb+=+11%2C%0D%0A%0D%0A%2810b+%2Ba%29+-+%2810a+%2B+b%29+=+9%29.

Now,  simplify it:

system+%28a%2Bb=+11%2C%0D%0A%0D%0A9b+-+9a+=+9%29.

Simplify it one more time:

system+%28a%2Bb=+11%2C%0D%0A%0D%0Ab+-+a+=+1%29.

Solve it.

The solution is   b=6,  a=5.

Hence,  the number is  10a + b = 10*5+6 = 56.