SOLUTION: the sume of a three-digit number is 11. The tens digit is three times the hundreds digit and two times the units digit. find the number.

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Question 712674: the sume of a three-digit number is 11. The tens digit is three times the hundreds digit and two times the units digit. find the number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the hundreds digit
Let +b+ = the tens digit
Let +c+ = the units digit
given:
(1) a+%2B+b+%2B+c+=+11+
(2) +b+=+3a+
(3) +b+=+2c+
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(2) +a+=+b%2F3+
(3) +c=+b%2F2+
Substitute (2) and (3) into (1)
(1) a+%2B+b+%2B+c+=+11+
(1) +b%2F3+%2B+b+%2B+b%2F2+=+11+
Multiply both sides by +6+
(1) +2b+%2B+6b+%2B+3b+=+66+
(1) +11b+=+66+
(1) +b+=+6+
and
(2) +a+=+b%2F3+
(2) +a+=+6%2F3+
(2) +a+=+2+
and
(3) +c=+b%2F2+
(3) +c=+6%2F2+
(3) +c+=+3+
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The number is 263