Question 107696: The sum of three consecutive odd integers is 201. Find the integers.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let x represent the first odd integer. The second consecutive odd integer must be 2 units
above the first. Therefore, the second odd integer is x + 2. And the third odd integer is
2 units above the second. So it is at x + 2 + 2 = x + 4. In summary, the three consecutive
odd integers are x, x + 2, and x + 4.
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If you add these together, the problem tells you that their sum is 201. In equation
form this is:
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x + x + 2 + x + 4 = 201
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When you collect like terms the left side becomes:
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(x + x + x) + (2 + 4) = 201
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This simplifies to:
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3x + 6 = 201
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Get rid of the 6 on the left side by subtracting 6 from both sides of the equation.
This subtraction results in the equation becoming:
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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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So the first odd integer is 65. Therefore the three consecutive odd integers are 65, 67, and 69.
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Check: does the sum of these three consecutive odd integers = 201? Yes, 65 + 67 + 69 does
equal 201. Therefore, our answer is correct.
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Hope this helps you to understand the problem.
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