Question 77178: The sum of three consecutive odd integers is 201. Find the integers.
Please help!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let x be the first odd integer. Then the next two consecutive odd integers are x + 2 and x + 4.
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Then, according to the problem, the sum of these three integers is 201. In equation form
this becomes:
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x + (x + 2) + (x + 4) = 201
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Collecting like terms on the left side results in:
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3x + 6 = 201
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Eliminate the 6 on the left side by subtracting 6. But if you subtract 6 on the left side
you must also subtract 6 on the right side. After this subtraction the equation becomes:
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3x = 195
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Solve for x by dividing both sides by 3 to get:
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x = 195/3 = 65
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Finally, if the first odd integer is 65, then the next two are 67 and 69
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Check by adding 65 + 67 + 69. You will find that this sum is 201, just as specified
by the problem.
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Hope this helps you to understand the method of working problems involving a series of
odd integers. The tricky part of this is realizing that successive odd integers are 2 units
apart on the number line because an even integer is tucked in between them.
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