SOLUTION: The sum of the digits of a two digit number is 12 .if the digits are interchange the number is increased by 36 .find the numbers

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Question 1208879: The sum of the digits of a two digit number is 12 .if the digits are interchange the number is increased by 36 .find the numbers
Answer by Alan3354(69443) About Me  (Show Source):
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The sum of the digits of a two digit number is 12 .if the digits are interchange the number is increased by 36 .find the numbers
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The increase or decrease from swapping the digits is 9 times the difference of the 2 digits.
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so,
x + y = 12
x - y = 36/9 = 4
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2x = 16
x = 8, y = 4
---> the number is 48
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w/o using the knowledge of 9 times the difference:
10T + U + 36 = T + 10U
9T - 9U = -36
T - U = -4
T + U = 12
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2T = 8
etc