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?

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) (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.
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