SOLUTION: three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. what are the integers?

Question 209550: three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. what are the integers?
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. what are the integers?
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1st: 2x-2
2nd: 2x
3rd: 2x+2
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Equation:
2x-2 +3(2x)= 2x+2+38
2x-2 + 6x = 2x +40
6x = 42
x = 7
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1st: 14-2 = 12
2nd: 14
3rd: 14+2 = 16
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Cheers,
Stan H.
Reply to stanbon@comcast.net
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Let the smallest integer be I
Then the 2nd and 3rd are (I + 2) and (I + 4)
Since the sum of the smallest and 3 times the second is 38 more than twice the 3rd, then we get:

I + 3(I + 2) = 2(I + 4) + 38

I + 3I + 6 = 2I + 8 + 38
4I � 2I = 46 � 6
2I = 40
I = 20
The integers are:
------------
Check
------------
20 + 3(22) = 2(24) + 38
20 + 66 = 48 + 38
86 = 86

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