SOLUTION: The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number. Thankyou :)))))))))

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Question 954258: The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number. Thankyou :)))))))))
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tens digit = +a+
Let the units digit = +b+
-------------------------
(1) +a+%2B+b+=+11+
(2) +10b+%2B+a+=+10a+%2B+b+%2B+45+
------------------------------
(2) +-9a+%2B+9b+=+45+
(2) +-a+%2B+b+=+5+
-------------------
Add (1) and (2)
+2b+=+16+
+b+=+8+
and
(1) +a+%2B+b+=+11+
(1) +a+=+11+-+b+
(1) +a+=+11+-+8+
(1) +a+=+3+
---------------
The number is 38
--------------------
check:
With digits reversed: 83
+83+-+38+=+45+
83 is 45 more than 38
OK