SOLUTION: a two digit number is such that the tens digit exceeds twice the unit digit by 2 and the number obtained by inter changing the digit is 5 more than three times the sum of the digit

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Question 804199: a two digit number is such that the tens digit exceeds twice the unit digit by 2 and the number obtained by inter changing the digit is 5 more than three times the sum of the digit, find the two digit 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
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(1) +t+=+2u+%2B+2+
(2) +10u+%2B+t+=+3%2A%28+t+%2B+u+%29+%2B+5+
----------------------------
(2) +10u+%2B+t+=+3t+%2B+3u+%2B+5+
(2) +7u+-+2t+=+5+
By substitution:
(2) +7u+-+2%2A%28+2u+%2B+2+%29+=+5+
(2) +7u+-+4u+-+4+=+5+
(2) +3u+=+9+
(2) +u+=+3+
and
(1) +t+=+2u+%2B+2+
(1) +t+=+2%2A3+%2B+2+
(1) +t+=+8+
The number is 83
check:
(2) +10u+%2B+t+=+3%2A%28+t+%2B+u+%29+%2B+5+
(2) +10%2A3+%2B+8+=+3%2A%28+8+%2B+3+%29+%2B+5+
(2) +38+=+3%2A11+%2B+5+
(2) +38+=+38+
OK