SOLUTION: The sum of the digits of a 2-digit number is 7. If 27 is added to the number, the resulting number has the same digits in the reverse order. What is the number?

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Question 132278: The sum of the digits of a 2-digit number is 7. If 27 is added to the number, the resulting number has the same digits in the reverse order. What is the number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 10s place digit = a
Let the 1s place digit = b
a+%2B+b+=+7
a+=+7+-+b
10a+%2B+b+%2B+27+=+10b+%2B+a
10%287+-+b%29+%2B+b+%2B+27+=+10b+%2B+7+-+b
70+-+10b+%2B+b+%2B+27+=+9b+%2B+7
-9b+%2B+97+=+9b+%2B+7
18b+=+90
b+=+5
a+=+7+-+b
a+=+2
The number is 25
check:
10a+%2B+b+%2B+27+=+10b+%2B+a
10%2A2+%2B+5+%2B+27+=+10%2A5+%2B+2
25+%2B+27+=+52
52+=+52
OK