SOLUTION: A two-digit number is obtained either by subtracting 12 from 4 times the sum of the digits or by adding 6 to twice of the differnce of its digits.find the number?

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Question 841078: A two-digit number is obtained either by subtracting 12 from 4 times the sum of the digits or by adding 6 to twice of the differnce of its digits.find the number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tens digit = +t+
Let the units digit = +u+
+10t+%2B+1%2Au+=+4%2A%28+t+%2B+u+%29+-+12+
+10t+%2B+1%2Au+=+2%2A%28+u+-+t+%29+%2B+6+
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I'm assuming that the units digit is
greater than the tens digit
By substitution, I can say:
+4%2A%28+t+%2B+u+%29+=+2%2A%28+u+-+t+%29+%2B+6+
+4t+%2B+4u++=+2u+-+2t+%2B+6+
+6t+%2B+2u+=+6+
+3t+%2B+u+=+3+
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+t+=+1+ and +u+=+0+ works
the number is 10
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check answer:
+4%2A%28+t+%2B+u+%29+=+2%2A%28+u+-+t+%29+%2B+6+
+4%2A%28+1+%2B+0+%29+=+2%2A%28+0+-+1+%29+%2B+6+
+4+=+-2+%2B+6+