SOLUTION: the sum of the two digit number is 7, when you reversed the number it was increased by 27. what is the original number?

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Question 212119: the sum of the two digit number is 7, when you reversed the number it was increased by 27. what is the original number?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A*10+B is the original number where A and B are between 0 and 9.
1. A+B=7
B*10+B is the number with digits reversed.
B*10+A=A*10+B+27
10B+A=10A+B+27
2.-9A+9B=27
Use eq. 1 to solve for A as a function of B.
A+B=7
A=7-B
Now substitute into eq. 2 and solve for B,
-9(7-B)+9B=27
-63+9B+9B=27
18B=90
B=5
Now go back and solve for A.
A=7-B
A=7-5
A=2
The original number was 25, the reversed digit number was 52.