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Anonymous asked in Science & MathematicsMathematics · 1 month ago

find three consecutive odd integers such that the sum of the first and the third equals the sum of the second and 13?

16 Answers

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  • TomV
    Lv 7
    1 month ago

    If you have 3 consecutive odd integers, the central integer is the mean of the two end integers. Hence the sum of the two end integers is twice the central integer. If the sum is the central integer plus 13, it is obvious the central integer must be 13.

    The three integers are 11, 13, 15.

    The same argument holds true if the set of integers are consecutive even integers or are any set of integers separated by a constant interval.

    Assume the integers are:

    n, n+a, n+2a

    The sum of the two end integers is n + n+2a = 2n+2a = 2(n+a)

    This is obviously double the central integer. The numbers don't even have to be integers. They can be any numbers. The necessary condition is that they be separated by a constant interval.

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  • Anonymous
    1 month ago

    Can you pls restate I didn’t really get that

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  • 1 month ago

    (2n + 1) + (2n + 5) =2n + 3 + 13

    4n + 6 = 2n + 16

    4n - 2n = 16 - 6

     2n = 10

     n = 5 answer//

    so

    2n + 1 = 2(5) + 1 = 11

    2n + 3 = 2(5) + 3 = 13

    2n + 5 = 2(5) + 5 = 15

    the odd integers are: 11, 13,15 ... answer//

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  • sepia
    Lv 7
    1 month ago

    Three consecutive odd integers such that 

    the sum of the first and the third equals 

    the sum of the second and 13:

    11, 13. and 15

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  • 1 month ago

    1st integer = (x + 1) 

    2nd integer = (x + 3)

    3rd integer = (x + 5)

    1st integer + 3rd integer = 2nd integer + 13 

    (x + 1) + (x + 5) = (x + 3) + 13 

    2x + 6 = x + 16

    2x = x + 10

    x = 10 

    1st integer = 10 + 1 = 11

    2nd integer = 10 + 3 = 13

    3rd integer = 10 + 5 = 15

     

    hope this helps! 

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  • Elaine
    Lv 7
    1 month ago

    Let the odd integers be n, n +2, n + 4

    n + (n + 4) = (n + 2) + 13

    2n + 4 = n + 15

    2n - n = 15 - 4

    n = 11

    The integers are 11, 13 15

    Verify

    11 + 15 = 26

    13  + 13 = 26 

    FYI

    n, n +2, n + 4 works for consecutive even integers as well 

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  • 1 month ago

    Let n be the first odd integer.

    Let n+2 be the second odd integer.

    Let n+4 be the third odd integer.

    "The sum of the first and the third..."

    n + n+4 

    "...equals the sum of the second and 13"

    n + n+4 = n+2 + 13

    2n + 4 = n + 15

    2n - n = 15 - 4

    n = 11

    Answer:

    11, 13, 15

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  • 1 month ago

    Let the first integer be 2n + 1.

    Then, the second integer is 2n + 3.

    The third integer is 2n + 5.

    So, (2n + 1) + (2n + 5) = (2n + 3) + 13

    Adding up each side:

    4n + 6 = 2n + 16, or simplify to:

    2n + 3  = n + 8

    n = 5

     

    so, the first odd number is:

    2n + 1 = (2 X 5) + 1 = 11

    and the other odd numbers would be 13 and 15

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  • DWRead
    Lv 7
    1 month ago

    (2n+1) + (2n+5) = (2n+3) + 13

    4n + 6 = 2n + 16

    n = 5

    2n+1 = 11

    2n+3 = 13

    2n+5 = 15

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  • 1 month ago

    let the integers be

    2n + 1, 2n + 3, 2n + 5

    then 4n + 6 = 2n + 16

    ==> 2n = 10

    ==> n = 5

    so

    11, 13 and 15

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