SOLUTION: For three consecutive odd integers, the sum of the least and the greatest is 146. What is the sum of all three integers? I don't even know where to start. Thank you for you tim

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Question 125145: For three consecutive odd integers, the sum of the least and the greatest is 146. What is the sum of all three integers?
I don't even know where to start.
Thank you for you time.
Found 2 solutions by josmiceli, bucky:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the smallest odd integer
n+%2B+2 will be the next greater odd integer
n+%2B+4 will be the next higher odd integer
n+%2B+%28n+%2B+4%29+=+146
2n+=+142
n+=+71
n+%2B+2+=+73
n+%2B+4+=+75
The consecutive odd integers are 71,73,75
check:
n+%2B+%28n+%2B+4%29+=+71+%2B+75
146+=+146
OK

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the first odd integer. Then the next consecutive odd number has to be 2 more
than x. This means that the next consecutive odd integer after x is x + 2. And the next consecutive
odd integer is 2 more than x + 2. So it has to be (x + 2) + 2 = x + 4
.
[Just to help understand this concept, let's look at three consecutive odd integers.
Say we choose 27 as the first odd integer. The next consecutive odd integer is 29 and that
is 2 more than 27. And the next consecutive odd integer is 31. This is equal to the first
odd integer in the series (27) plus 4.]
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Now back to the problem. We have three consecutive odd integers which are x, x + 2, and x + 4.
.
The problem tells you that the sum of the least (which is x) and the greatest (which is x + 4)
is 146. In equation form this is:
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x + (x + 4) = 146
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If we add the two terms on the left side we get 2x + 4 and the equation is then:
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2x + 4 = 146
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Get rid of the +4 on the left side by subtracting 4 from both sides to get:
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2x = 142
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Solve for x by dividing both sides by 2 to get:
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x = 142/2 = 71
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x was defined as the first odd integer. Therefore, the next two consecutive odd integers are
73 and 75.
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Add the smallest odd integer (71) to the greatest odd integer (75) and you get a total of
146 just as the problem said you should. So the answer checks.
.
And you were asked to find the sum of all three. So all you have to do now is to add the three
consecutive odd integers:
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71 + 73 + 75 = 219
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The answer to this problem is 219
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Hope this helps you to understand the problem and how you would do it.
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