SOLUTION: The sum of the digits is 12. The original number decreased by 36 equals the number formed when the digits are reversed. Find the original number

Algebra ->  Linear-equations -> SOLUTION: The sum of the digits is 12. The original number decreased by 36 equals the number formed when the digits are reversed. Find the original number       Log On


   

Question 1116198: The sum of the digits is 12. The original number decreased by 36 equals the number formed when the digits are reversed. Find the original number
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
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Let the tens digit = +t+
Let the units digit = +u+
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(1) +t+%2B+u+=+12+
(2) +10t+%2B+u+-+36+=+10u+%2B+t+
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(2) +9t+-+9u+=+36+
(2) +t+-+u+=+4+
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Add (1) and (2)
(1) +t+%2B+u+=+12+
(2) +t+-+u+=+4+
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+2t+=+16+
+t+=+8+
and
(1) +8+%2B+u+=+12+
(1) +u+=+4+
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The original number is 84
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check:
+84+-+36+=+48+
The digits are reversed
OK

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the digits is 12. The original number decreased by 36 equals the number formed when the digits are reversed. Find the original number
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Swapping the digits of a 2 digit number changes is value by 9 times the difference between the digits.
--> difference = 4
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T + U = 12
T - U = 4
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