SOLUTION: a number is less than 100 and its tens digit is 2 more than its units digit. if the number with the digits reversed is subtracted from the original number , the remainder is 3 time

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Question 1037150: a number is less than 100 and its tens digit is 2 more than its units digit. if the number with the digits reversed is subtracted from the original number , the remainder is 3 times the sum of the digits. find the 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+=+u+%2B+2+
(2) +10t+%2B+u+-+%28+10u+%2B+t+%29+=+3%2A%28+t+%2B+u+%29+
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Substitute (1) into (2)
(2) +10%2A%28+u+%2B+2+%29+%2B+u+-+%28+10u+%2B+u+%2B+2+%29+=+3%2A%28+u+%2B+2+%2B+u+%29+
(2) +10u+%2B+20+%2B+u+-+11u+-+2+=+3%2A%28+2u+%2B+2+%29+
(2) +11u+%2B+20+-+11u+-+2+=+6u+%2B+6+
(2) +20+-+2+=+6u+%2B+6+
(2) +18+=+6u+%2B+6+
(2) +6u+=+12+
(2) +u+=+2+
and
(1) +t+=+u+%2B+2+
(1) +t+=+4+
The number is 42
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check:
Number with digits reversed: 24
+42+-+24+=+18+
+18+=+3%2A%28+4+%2B+2+%29+
+18+=+3%2A6+
+18+=+18+
OK