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Question 498048: What are three even consecutive integers when the sum of the first and four times the third equals 52?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Something is amiss with this problem.
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Let's begin by doing what the problem tells you to do.
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Begin with the fact that consecutive even numbers are separated by 2. (Think 2, 4, 6, ...). Therefore, if N is the first even number, the next (second) consecutive even number is N + 2 and the third consecutive even number is N+4.
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The sum of the first even number and four times the third can then be written as:
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N + 4*(N+4)
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and the problem tells you that this sum is to equal 52. So you can write the equation:
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N + 4*(N+4) = 52
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Do the distributed multiplication on the left side to get:
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N + 4N + 16 = 52
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Add the terms containing N to get:
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5N + 16 = 52
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Get rid of the 16 on the left side by subtracting 16 from both sides:
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5N + 16 - 16 = 52 - 16
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Do the subtractions and get:
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5N = 36
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Solve for N by dividing by 5 and you have:
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N = 7.2
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This is not an integer. And it is closer to being odd than it is to being even. Something is wrong with the way the problem is set up.
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As a check, let's try something in the vicinity of this answer to see what might happen. Begin by assuming that the series of consecutive even numbers is 6, 8, and 10. This means that the sum of the first and four times the third is 6 +(4*10) = 46. Well, that sum is too small. The series needs to be a little more. So let's up the series by saying that the first even integer is 8 and the three terms are then 8, 10, and 12. That means that the sum of the first term and four times the third is 8 + (4*12) = 56. That's too big and it would only get bigger (and more in error) by raising the series again to 10, 12, and 14. So there is no correct answer to this problem as it is currently written.
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The method of solving it is correct. Perhaps the total should have been 56 instead of 52. This could be verified by replacing 52 with 56 in the above work to get:
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N + 4*(N+4) = 56
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Do the distributed multiplication on the left side to get:
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N + 4N + 16 = 56
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Add the terms containing N to get:
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5N + 16 = 56
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Get rid of the 16 on the left side by subtracting 16 from both sides:
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5N + 16 - 16 = 56 - 16
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Do the subtractions and get:
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5N = 40
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Solve for N by dividing by 5 and you have:
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N = 8
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And this means that the series should be 8, 10, and 12 as noted in the analysis above.
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I hope this helps you to understand the problem a little better and to see why it is wrong as written.
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