SOLUTION: The tens digit of a two digit number is 2 less than twice the ones digit. If the number is reversed, the new number is 18 less than the original number

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Question 515818: The tens digit of a two digit number is 2 less than twice the ones digit. If the number is reversed, the new number is 18 less than the original number
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the tens digit
Let b = the ones digit
given:
+a+=+2b+-+2+
+a+=+2%2A%28+b-1%29+
+10a+%2B+b+ is the original number
+10b+%2B+a+ is the reverse of the number
+10b+%2B+a+=+10a+%2B+b+-+18+
+10%2A%28a-b%29+%2B+b-a+=+18+
+10%2A%28a-b%29+%2B+b-a+=+18+
+10a+-+10b+%2B+b+-+a+=+18+
+9a+-+9b+=+18+
+a+-+b+=+2+
By substitution:
+2%2A%28b-1%29+-+b+=+2+
+2b+-+2+-+b+=+2+
+b+=+4+
and
+a+=+2%2A%28+b-1%29+
+a+=+2%2A3+
+a+=+6+
The original number is 64
check:
Reverse the digits: 46
64 = 46 + 18
OK