SOLUTION: The sum of the digits of a certain 2 digit number is 11. Reversing its digits increases the number by 63. Find the number.

Algebra ->  Sequences-and-series -> SOLUTION: The sum of the digits of a certain 2 digit number is 11. Reversing its digits increases the number by 63. Find the number.      Log On


   



Question 539342: The sum of the digits of a certain 2 digit number is 11. Reversing its digits increases the number by 63. Find the number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 10's digit = a
Let the 1's digit = b
given:
(1) +a+%2B+b+=+11+
(2) +10b+%2B+a+=+10a+%2B+b+%2B+63+
--------------------------
(2) +10b+-+b+-+10a+%2B+a+=+63+
(2) +9b+-+9a+=+63+
(2) +b+-+a+=+7+
(1) +b+%2B+a+=+11+
Add the equations
+2b+=+18+
+b+=+9+
And, since
(1) +a+%2B+b+=+11+
(1) +a+%2B+9+=+11+
(1) +a+=+2+
The number is 29