SOLUTION: a two digit number increases by 27 when it is reversed. the unit digit is 1 greater than 3 times the ten digit. Find the number

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Question 544540: a two digit number increases by 27 when it is reversed. the unit digit is 1 greater than 3 times the ten digit. Find the number
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = tens digit
Let +b+ = units digit
+10a+%2B+b+ = the value of the number
given:
(1) +10b+%2B+a+=+10a+%2B+b+%2B+27+
(2) +b+=+3a+%2B+1+
------------------
(1) +-9a+%2B+9b+=+27+
(1) +-a+%2B+b+=+3+
(2) +-3a+%2B+b+=+1+
Subtract (2) from (1)
(1) +-a+%2B+b+=+3+
(2) +3a+-+b+=+-1+
+2a+=+2+
+a+=+1+
and, since
(2) +b+=+3a+%2B+1+
(2) +b+=+3%2A1+%2B+1+
(2) +b+=+4+
The number is 14
Check answer:
(1) +10b+%2B+a+=+10a+%2B+b+%2B+27+
(1) +10%2A4+%2B+1+=+10%2A1+%2B+4+%2B+27+
(1) +41+=+14+%2B+27+
(1) +41+=+41+
OK