SOLUTION: The sum of the digits of a ccertain two digit number is 7. Reversing its digits increases the number by 9. What is the number??

Question 695781: The sum of the digits of a ccertain two digit number is 7. Reversing its digits increases the number by 9. What is the number??
Answer by henew(13) (Show Source): You can put this solution on YOUR website!

Take 2 digits as a and b
we know a+b=7
The original number is written as 10a+b ( Take example of 37, the number is 3 x10+7)
When you reverse the number new number is 10b+a.
We have 10b+a = (10a+b)+9
10b+a=10a+b+9
9a-9b= -9
so we have 2 equations
a+b=7 and 9a-9b=-9
multiply 1 by 9
9a+9b=63
9a-9b= -9
18a=54
a=3, so b=4
number is 34.
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