SOLUTION: find three consecutive integers such that the first added to 5 times the second exceeds 3 times the last by 51.

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Question 694690: find three consecutive integers such that the first added to 5 times the second exceeds 3 times the last by 51.
Answer by 55305(86) About Me  (Show Source):
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First lets assume the three number are n-1,n,and n+1, since the numbers are consecutive integers. Our equation would be
%28n-1%29%2B+5%2An=+3%28n%2B1%29%2B51, which simplifies to
6%2An-1=3%2An%2B54. Now we can solve by subtracting 3n and adding 1 to each side:
3%2An=55
that would mean that n is not an integer, and there are no consecutive integers which have those properties.
Numbers that work out that differ by 1 are 52%2F3 55%2F3 58%2F3