SOLUTION: The units digit of a 2-digit number is one more than twice the tens digit.The sum of the original number and the number represented when the digit are interchanged is 77. Find the

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Question 1126456: The units digit of a 2-digit number is one more than twice the tens digit.The sum of the original number and the number represented when the digit are interchanged is 77. Find the original number
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +u+ = the units digit of the original number
Let +t+ = the tens digit of the original number
-------------------------
(1) +u+=+2t+%2B+1+
(2) +10t+%2B+u+%2B+10u+%2B+t+=+77+
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Multiply both sides of (1) by +11+ and add
(1) +2t+-+u+=+-1+
(2) +11t+%2B+11u+=+77+
(1) +22t+-+11u+=+-11+
------------------------------
+33t+=+66+
+t+=+2+
and
(1) +u+=+2t+%2B+1+
(1) +u+=+2%2A2+%2B+1+
(1) +u+=+5+
-------------------------
the number is 25
--------------------------
check{
(2) +11t+%2B+11u+=+77+
(2) +11%2A2+%2B+11%2A5+=+77+
(2) +22+%2B+55+=+77+
(2) +77+=+77+
OK