SOLUTION: A two-digit number is three times the sum of it’s digits. When the number is subtracted from the number obtained by reversing the digits, the result is 45. Find the original numb

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Question 1146480: A two-digit number is three times the sum of it’s digits. When the number is subtracted from the number obtained by reversing the digits, the result is 45. Find the original number.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The two-digit number: 10t%2Bu

First Sentence:
10t%2Bu=3%28t%2Bu%29
10t%2Bu=3t%2B3u
7t=2u

Second Sentence:
t%2B10u-%2810t%2Bu%29=45
-9t%2B9u=45
-t%2Bu=5

This system should be easy to work with and solve.
Some logic may also be useful...
system%287t=2u%2Cu-t=5%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the tens digit of the original number
Let +u+ = the units digit of the original number
--------------------------------------------------------
(1) +10t+%2B+u+=+3%2A%28+t+%2B+u+%29+
(2) +10u+%2B+t+-+%28+10t+%2B+u+%29+=+45+
-----------------------------------------
(1) +10t+%2B+u+=+3t+%2B+3u+
(1) +7t+=+2u+
(1) +u+=+%287%2F2%29%2At+
and
(2) +10u+%2B+t+-+10t+-+u+=+45+
(2) +9u+-+9t+=+45+
(2) +9%2A%28+u+-+t+%29+=+45+
(2) +u+-+t+=+5+
and
(2) +%287%2F2%29%2At+-+t+=+5+
(2) +%285%2F2%29%2At+=+5+
(2) +t+=+10%2F5+
(2) +t+=+2+
and
(2) +u+-+t+=+5+
(2) +u+-+2+=+5+
(2) +u+=+7+
-----------------------
The original number is 27
---------------------------------
check:
(1) +27+=+3%2A%28+2+%2B+7+%29+
(1) +27+=+27+
and
(2) +72+-+27+=+45+
(2) +45+=+45+
OK