SOLUTION: A number consists of two digits whose sum is 9. the number formed by reversing the digits exceeds twice the original number by 18. find the original number.

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Question 803222: A number consists of two digits whose sum is 9. the number formed by reversing the digits exceeds twice the original number by 18. find the original number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tens digit = +t+
Let the units digit = +u+
------------
'(1) +t+%2B+u+=+9+
(2) +10u+%2B+t+=+2%2A%28+10t+%2B+u+%29+%2B+18+
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(2) +10u++%2B+t+=+20t+%2B+2u+%2B+18+
(2) +10u+-+2u+%2B+t+-+20t+=+18+
(2) +8u+-+19t+=+18+
and, since
'(1) +t+%2B+u+=+9+
(1) +u+=+9+-+t+
By substitution:
(2) +8%2A%28+9+-+t+%29+-+19t+=+18+
(2) +72+-+8t+-+19t+=+18+
(2) +-27t+=+-54+
(2) +t+=+2+
and
(1) +u+=+9+-+t+
(1) +u+=+7+
The original number is 27
----------------------
check:
Reverse digits: +72+
+72+=+2%2A%28+27+%29+%2B+18+
+72+=+54+%2B+18+
+72+=+72+
OK