SOLUTION: Find four consecutive even integers such that twice the sum of the second and third exceeds 3 times the first by 34.

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Question 401571: Find four consecutive even integers such that twice the sum of the second and third exceeds 3 times the first by 34.
Answer by MathLover1(20850) About Me  (Show Source):
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four consecutive even integers
n,
%28n+%2B+2%29,
%28n+%2B+4%29 and
%28n+%2B+6%29

twice the sum of the second and third:
2%28%28n+%2B+2%29%2B%28n+%2B+4%29%29=2%282n%2B6%29=4n%2B12
exceeds 3 times ,3n the first by 34
or
4n%2B12=3n%2B34
4n%2B12-3n=3n-3n%2B34

n%2B12-12=34-12
n=22....first number
n+%2B+2=22%2B2=24, .....second
n+%2B+4=22%2B4=26 .......third
and
n+%2B+6=22%2B6=28..........fourth

check:
twice the sum of the second and third: 2%2824%2B26%29=2%2A50=100
3 times the first: 3n=3%2A22=66
exceeds by: 100-66=34