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Math Help - consecutive integers help

  1. #1
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    Question consecutive integers help

    find three consecutive integers such that the sum of the first and the third is 80?





    the difference of two numbers is 46.the larger of the two numbers is 3 times the smaller. find the value of the two numbers.
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  2. #2
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    Quote Originally Posted by BeBeMala View Post
    find three consecutive integers such that the sum of the first and the third is 80?

    let x = the first integer ...

    x + (x+2) = 80

    the difference of two numbers is 46.the larger of the two numbers is 3 times the smaller. find the value of the two numbers.

    x - y = 46

    x = 3y
    ...
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  3. #3
    Super Member Bacterius's Avatar
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    Say your two consecutive numbers are :

    x, x + 1 and x + 2

    The sum of the first and the third is 80, so x + x + 2 = 80, which simplifies to 2x + 2 = 80, or 2x = 78, and finally x = 39. Substitute back this value into your consecutive integers. Your consecutive integers are :

    39, 39 + 1 and 39 + 2, that is, your integers are 39, 40 and 41.

    --

    Say the two numbers are x and y, such as x > y.

    - Their difference is 46, so x - y = 46.

    - The larger of the two numbers ( x) is 3 times the smaller ( y), so x = 3y.

    You have x - y = 46, and y = 3x. Substitute the second into the first :

    (3y) - y = 46

    Which simplifies to :

    2y = 46

    Thus y = 23.

    Plug this back into the first equation to find x :

    x - (23) = 46, so x = 46 + 23 = 69.

    Your two numbers are 23 and 69.
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