SOLUTION: find three consecutive odd integers such that the sum of the first integer, twice the second integer, and four times the third is 97.

Question 489517: find three consecutive odd integers such that the sum of the first integer, twice the second integer, and four times the third is 97.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Each consecutive odd integer is separated by adding 2 to its preceding odd integer. For example: odd integers 3, 5, 7, and 9 are consecutive odd integers. Note that 5 is 3 + 2 and 7 is 5 + 2 and 9 is 7 + 2.
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Therefore, if N is an odd integer, the next consecutive odd integer is N+2 and the next consecutive odd integer after that is (N+2) + 2 and this can be simplified to N + 2 + 2 which is N+4. So we can say that three consecutive odd numbers are N, N+2, and N+4.
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The problem then describes three terms as follows:
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The first term is the first odd integer or N.
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The second term is twice the second odd integer or twice N+2. If you multiply N+2 by 2 the result is 2N+4.
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The third term is 4 times the third odd integer. This would be 4 times N+4. If you multiply 4*(N+4) the result is 4N+ 16.
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You are then to add these three terms and you are told that the answer is 97. When written in equation form this is:
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N + (2N + 4) + (4N + 16) = 97
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Group the terms containing N and separately group the constants and the equation becomes:
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(N + 2N + 4N) + (4 + 16) = 97
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Add the terms containing N and also add the constants and the equation simplifies to:
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7N + 20 = 97
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Get rid of the 20 on the left side of the equation by subtracting 20 from both sides to get:
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7N + 20 - 20 = 97 - 20
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and the subtractions simplify this equation to:
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7N = 77
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Solve for N by dividing both sides by 7 and the result is:
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N = 11
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So now we know that N, the first odd integer, is 11. This means that the second consecutive odd integer is 2 greater than 11 or it is 13 and the third consecutive odd integer is 2 greater than 13 or it is 15.
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So the three consecutive odd integers you were to find are 11, 13, and 15.
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Check this by adding the first odd integer (11) to two times 13 or (26) to 4 times 15 or (60).
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11 + 26 + 60
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If you add these three numbers, the sum is 97 just as the problem said it should be. Therefore, the answer is correct. The three consecutive odd integers the problem was looking for are 11, 13, and 15.
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Hope this helps you to understand the problem.
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