SOLUTION: A certain two-digit number is 2 less than three times the sum of its digit. If 54 is added to the number, the number would be reversed. Find the number.

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Question 1087040: A certain two-digit number is 2 less than three times the sum of its digit. If 54 is added to the number, the number would be reversed. Find the number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +u+ = the units digit
Let +t+ = the tens digit
----------------------------
(1) +10t+%2B+u+=+3%2A%28+t+%2B+u+%29+-+2+
(2) +10t+%2B+u+%2B+54+=+10u+%2B+t+
--------------------------------
(1) +10t+%2B+u+=+3t+%2B+3u+-+2+
(1) +7t+-+2u+=+-2+
and
(2) +9t+-+9u+=+-54+
(2) +t+-+u+=+-6+
-----------------------------
Multiply both sides of (2) by +2+
and subtract (2) from (1)
(1) +7t+-+2u+=+-2+
(2) +-2t+%2B+2u+=+12+
--------------------------
+5t+=+10+
+t+=+2+
and
(2) +t+-+u+=+-6+
(2) +2+-+u+=+-6+
(2) +-u+=+-8+
(2) +u+=+8+
--------------------
The number is 28
--------------------
check:
3 times the sum of it's digits:
+3%2A%28+2+%2B+8+%29+=+30+
+30+-+2+=+28+
OK
Add 54 to the number:
+28+%2B+54+=+82+
The number is reversed
OK