Yahoo Answers: Answers and Comments for Three consecutive odd integers have a sum of 45. what are the integers? [Mathematics]
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From Skittles.
enUS
Wed, 09 May 2012 15:33:30 +0000
3
Yahoo Answers: Answers and Comments for Three consecutive odd integers have a sum of 45. what are the integers? [Mathematics]
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From Keith Roberts: Hi Skittles,
Recall that you can take any i...
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Wed, 09 May 2012 15:43:05 +0000
Hi Skittles,
Recall that you can take any integer x, and turn it into an even integer by multiplying it by 2. Thus, you can always make it odd, by multiplying it by 2, and then adding 1. Thus, 2x + 1 is always odd.
So, if you want three consecutive odd integers, you can select:
(1) 2x + 1
(2) 2x + 1 + 2 = 2x + 3
(3) 2x + 1 + 2 + 2 = 2x + 5
Now just add them together and set them equal to 45:
(2x + 1) + (2x + 3) + (2x + 5) = 6x + 9,
so 6x + 9 = 45. Now solve, to find that x = 9.
Now remember that x = 9 is not our answer, we have to use x to find the first consecutive odd: 2*9 + 1 = 17. Our next two consecutive odds are then 15, and 13.
Check to see if these sum to 45? 17 + 15 + 13 = 45, check!
To help reinforce your understanding of these concepts, I've searched and found a webpage and a video tutorial that address problems similar to this one, and I thought they might be helpful to you. I've listed them below.
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From Liz: The three consecutive odd integers with sum of...
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Wed, 09 May 2012 15:38:36 +0000
The three consecutive odd integers with sum of 45 are:
13, 15, 17

From Ronen Wdowinski: 13, 15, 17
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Wed, 09 May 2012 15:38:16 +0000
13, 15, 17