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Math Help - Odd Integers

  1. #1
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    Odd Integers

    What is the product if the largest of three consecutive odd integers whose sum is 129 is multiplied by 4?

    Is the right equation:

    x + (x + 2) + 4(x + 4) = 129?
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  2. #2
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    no, first you need to find three consecutive odd integers whose sum is 129.

    let the three
    consecutive odd integers be (x-2),x,(x+2),
    so

    (x-2)+x+(x+2)=129

    solving this, you'll get x, and the largest odd integers is (x+2)
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  3. #3
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    but...

    Quote Originally Posted by dedust View Post
    no, first you need to find three consecutive odd integers whose sum is 129.

    let the three consecutive odd integers be (x-2),x,(x+2),
    so

    (x-2)+x+(x+2)=129

    solving this, you'll get x, and the largest odd integers is (x+2)
    I've always seen x, x + 2 and x + 4 used to represent consecutive odd integers. Where did (x - 2) come from?
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  4. #4
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    if you have x as the first number, then the second is x+2 but now if you have x as the second number then x-2 is the first,..is it clear??

    just the trick to solve the problem
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  5. #5
    Super Member Bacterius's Avatar
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    You can use whatever expressions provided that they are odd consecutives relative to x. You could have :

    (x + 88) and (x + 90) and (x + 92)

    or

    (x - 192) and (x - 190) and (x - 188)
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  6. #6
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    Quote Originally Posted by Bacterius View Post
    You can use whatever expressions provided that they are odd consecutives relative to x. You could have :

    (x + 88) and (x + 90) and (x + 92)

    or

    (x - 192) and (x - 190) and (x - 188)
    yes,..choose the number that make it easier to solve
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  7. #7
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    Ok...

    Quote Originally Posted by dedust View Post
    if you have x as the first number, then the second is x+2 but now if you have x as the second number then x-2 is the first,..is it clear??

    just the trick to solve the problem
    I thank you for this great trick and short cut. When I tried using my original equation, I ended up with 111/6, which didn't make sense to me at all.
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  8. #8
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    Ray...

    Quote Originally Posted by Bacterius View Post
    You can use whatever expressions provided that they are odd consecutives relative to x. You could have :

    (x + 88) and (x + 90) and (x + 92)

    or

    (x - 192) and (x - 190) and (x - 188)
    Can we also use x, x + 2 and x + 4 as the list of consecutive odd integers to solve this question? When I did the algebra, I ended up with x = 111/6, which did not make sense to me at all.


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  9. #9
    Super Member Bacterius's Avatar
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    Sure you can, but you got to rearrange your solution according to this at the end of your operations
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    Ray...

    Quote Originally Posted by Bacterius View Post
    Sure you can, but you got to rearrange your solution according to this at the end of your operations
    Can you demonstrate for me?
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  11. #11
    Super Member Bacterius's Avatar
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    Think about the meaning of x, and you should find out where something goes wrong
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  12. #12
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    Quote Originally Posted by sologuitar View Post
    Can we also use x, x + 2 and x + 4 as the list of consecutive odd integers to solve this question? When I did the algebra, I ended up with x = 111/6, which did not make sense to me at all.

    how do you get x = 111/6 ?


    Spoiler:
    x + (x+2) + (x+4) = 129
    3x + 6 = 129
    3x=123
    x=41
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  13. #13
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    I see...

    Quote Originally Posted by dedust View Post
    how do you get x = 111/6 ?


    Spoiler:
    x + (x+2) + (x+4) = 129
    3x + 6 = 129
    3x=123
    x=41
    I made simple algebra errors that led to the wrong answer for x. Thanks for showing me the right way to find x.
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