SOLUTION: What is the two‐digit number that satisfies the following conditions? The tens digit is larger than the units digit; the sum of the digits is 12; and if the digits are reversed a

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Question 1142971: What is the two‐digit number that satisfies the following conditions? The tens digit is larger than the units digit; the sum of the digits is 12; and if the digits are reversed and the resulting two‐digit number is subtracted from the original number, the difference is 18.
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+
+t+%3E+u+
+t+%2B+u+=+12+
+%28+10t+%2B+u+%29+-+%28+10u+%2B+t+%29+=+18+
-------------------------------------
+10t+%2B+u+-+10u+-+t+=+18+
+9t+-+9u+=+18+
+t+-+u+=+2+
+t+%2B+u+=+12+ ( add the equations )
--------------------
+2t+=+14+
+t+=+7+
and
+t+%2B+u+=+12+
+7+%2B+u+=+12+
+u+=+5+
--------------------
The number is 75
---------------------
check:
+%28+10t+%2B+u+%29+-+%28+10u+%2B+t+%29+=+18+
+75+-+57+=+18+
+18+=+18+
OK