SOLUTION: The sum of the digits of a two digit number is 11. When the digits are reversed, the new number is 27 less than the original number. Find the original number.

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Question 940664: The sum of the digits of a two digit number is 11. When the digits are reversed, the new number is 27 less than the original number. Find the original number.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
U and T the digits.
U%2BT=11

10U%2BT=-27%2B%2810T%2BU%29

Goal is to find 10T+U.


Simplify the second equation:
10U%2BT-U-10T=-27
9U-9T=-27
U-T=3

Summarize simplified system:
system%28T%2BU=11%2C-T%2BU=3%29
Ready for easy elimination method.
2U=14
highlight%28U=7%29
-
T=11-U
T=11-7
highlight%28T=4%29
-
The two-digit number is 47.