SOLUTION: the tens digit of a number is 3 less than the units digit. if the numbers is divided by the sum of the digits, the quotient is 4 and the remainder is 3. what is the original number

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Question 990808: the tens digit of a number is 3 less than the units digit. if the numbers is divided by the sum of the digits, the quotient is 4 and the remainder is 3. what is the original number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the tens digit
Let +u+ = the units digit
------------------------
(1) +t+=+u+-+3+
(2) +%28+10t+%2B+u+%29+%2F+%28+t+%2B+u+%29+=+4+%2B+3%2F%28+t+%2B+u+%29+
-------------------------------------
Multiply both sides of (2) by +t+%2B+u+
(2) +10t+%2B+u+=+4%2A%28+t+%2B+u+%29+%2B+3+
(2) +10t+%2B+u+=+4t+%2B+4u+%2B+3+
(2) +6t+-+3u+=+3++
(2) +2t+-+u+=+1+
and
(1) +-t+%2B+u+=+3+
Add (1) and (2)
-----------------
+t+=+4+
and
(1) +t+=+u+-+3+
(1) +4+=+u+-+3+
(1) +u+=+7+
The number is 47
-----------------
check:
(2) +%28+10t+%2B+u+%29+%2F+%28+t+%2B+u+%29+=+4+%2B+3%2F%28+t+%2B+u+%29+
(2) +%28+10%2A4+%2B7+%29+%2F+%28+4+%2B+7+%29+=+4+%2B+3%2F%28+4+%2B+7+%29+
(2) +47+%2F+11+=+4+%2B+3%2F11+
(2) +47+=+44+%2B+3+
(2) +47+=+47+
OK