SOLUTION: The sum of three consecutive integers equals the difference between 5 times the smallest and the largest. Find the integers.

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Question 1101595: The sum of three consecutive integers equals the difference between 5 times the smallest and the largest. Find the integers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 3 consecutive integers be
+n+, +n%2B1+, and +n+%2B+2+
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+n+%2B+n+%2B+1+%2B+n+%2B+2+=+5n+-+%28+n%2B2+%29+
+3n+%2B+3+=+5n+-+n+-+2+
+3n+=+4n+-+5+
+n+=+5+
and
+n+%2B+1+=+6+
+n+%2B+2+=+7+
The consecutive integers are 5, 6, and 7
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check:
+n+%2B+n+%2B+1+%2B+n+%2B+2+=+5n+-+%28+n%2B2+%29+
+5+%2B+6+%2B+7+=+5%2A5+-+7+
+18+=+25+-+7+
+18+=+18+
OK