SOLUTION: Sum of the digits of a two digit number is 10 when we interchange the digits it is found that the resulting number is greater than the original number by 36 PLAEASE H

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Question 989803: Sum of the digits of a two digit number is 10 when we interchange the digits it is found that the resulting number is greater than the original number by 36


PLAEASE HELP ME NOW ITS URGENT!!!!!!!!!!
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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Let a and b are the digits of your number  n,  so that  n = 10a + b.

The number after interchanging digits is  10b + a.

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

system%28a%2Bb+=+10%2C%0D%0A%0D%0A%2810b+%2Ba%29+-+%2810a+%2B+b%29+=+36%29.

Now,  simplify it:

system+%28a%2Bb=+10%2C%0D%0A%0D%0A9b+-+9a+=+36%29.

Simplify one more time:

system+%28a%2Bb=+10%2C%0D%0A%0D%0Ab+-+a+=+4%29.

Solve it.

b=7,  a=3.

The number is  10a + b = 10*3+7 = 37.

Answer.  37.