Question 126673: Find three consecutive odd integers whose sum is three times the third integer Found 2 solutions by bucky, solver91311:Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Consecutive odd integers are 2 digits apart (think of 3 and 5 and 7 as being consecutive
odd integers). So if we let x represent the first odd integer, the next consecutive odd
integer is x + 2 and the next consecutive odd integer after x + 2 is x + 4.
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Then three times the third integer is 3*(x + 4) which multiplies out to 3x + 12.
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The problem tells you that the sum of the three consecutive odd integers is 3 times the
third integer. In equation form this can be written as:
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x + (x + 2) + (x + 4) = 3x + 12
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On the left side of this equation combine the like terms to get:
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3x + 6 = 3x + 12
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What happens if you subtract 3x from both sides? This reduces the "equation" to
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6 = 12
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And that obviously cannot be and is not true. This tells you that there is no value of
x that will satisfy this problem. That further means that there are no 3 consecutive
odd integers that add together to give you a sum equal to 3 times the third of the three
consecutive odd integers.
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Hope this helps you to understand why you were having a problem with this exercise.
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You can put this solution on YOUR website! If the first odd integer is x, the second one would be x + 2, and the third one would be x + 4.
The sum of the three is but this is equal to 3 times the third odd integer
Adding -3x to both sides of the equation leads to the absurdity that . Therefore, there is no solution to the problem as stated.
Had the problem said 3 times the SECOND integer we would have achieved the result that -- true no matter what x is. Meaning that any three consecutive odd integers would exhibit the property that their sum is equal to 3 times the second integer. In fact, any three consecutive EVEN integers, or just any three consecutive integers also exhibit the same property.
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