Results 1 to 9 of 9
Like Tree7Thanks
  • 1 Post By topsquark
  • 1 Post By DenisB
  • 2 Post By greg1313
  • 2 Post By DenisB
  • 1 Post By greg1313

Thread: Number of Integers

  1. #1
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Number of Integers

    How many integers n is 7n+1 divisible by 3n+5?

    What exactly is this question asking?
    What's the set up?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,493
    Thanks
    899
    Awards
    1

    Re: Number of Integers

    Quote Originally Posted by harpazo View Post
    How many integers n is 7n+1 divisible by 3n+5?

    What exactly is this question asking?
    What's the set up?
    Hint: Do the long division $\displaystyle \dfrac{7n + 1}{3n + 5}$. You'll get a remainder that depends on n. How many values of n are there such that the remainder is 0?

    -Dan

    Addendum: Or you could just pick a bunch of n values and see how many work.
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,255
    Thanks
    500

    Re: Number of Integers

    Quote Originally Posted by harpazo View Post
    How many integers n is 7n+1 divisible by 3n+5?
    (7n - 1)/(3n + 5) = x
    solve for n:
    n = (5x - 1)/(7 - 3x)

    So (from denominator) 3x < 7 : see that??
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Dec 2016
    From
    Earth
    Posts
    282
    Thanks
    148

    Re: Number of Integers

    Quote Originally Posted by DenisB View Post
    (7n - 1)/(3n + 5) = x
    solve for n:
    n = (5x - 1)/(7 - 3x)

    So (from denominator) 3x < 7 : see that??
    n is not restricted to positive integers. If n = -2, for instance, then x = 13.
    Thanks from topsquark and harpazo
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,255
    Thanks
    500

    Re: Number of Integers

    Yep....so:
    n = -7 or -3 or -2 or -1 or 1 or 2
    Thanks from topsquark and harpazo
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Dec 2016
    From
    Earth
    Posts
    282
    Thanks
    148

    Re: Number of Integers

    Quote Originally Posted by DenisB View Post
    Yep....so:
    n = -7 or -3 or -2 or -1 or 1 or 2
    You have made two errors. First, you included n = 2, which does not work
    because the fraction equals 15/11, a noninteger. Second, you did not include the
    solution of n = 9, which makes the fraction 64/32 = 2.

    Also, I did not catch your typo in the numerator of your fraction.
    Instead of (7n - 1) that you wrote, it is supposed to be (7n + 1).
    However, the expression for n in terms of x right below that is correct.
    Last edited by greg1313; Dec 24th 2018 at 08:03 PM.
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Number of Integers

    Thank you everyone.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,255
    Thanks
    500

    Re: Number of Integers

    Yikes...my "2" should be "9" (typo).

    -7 -48/-16 3
    -3 -20/-4 5
    -2 -13/-1 13
    -1 -6/2 -3
    1 8/8 1
    9 64/32 2

    Hope that's typoless!

    Thanks Greg.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Number of Integers

    Good notes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. number of integers bet 90 and 990
    Posted in the Algebra Forum
    Replies: 9
    Last Post: Dec 23rd 2012, 10:36 PM
  2. Real number division using integers
    Posted in the Math Software Forum
    Replies: 2
    Last Post: Jul 19th 2011, 12:55 AM
  3. Replies: 2
    Last Post: Jul 18th 2010, 02:57 PM
  4. Find the number of integers
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Nov 30th 2009, 06:55 PM
  5. number of ways to add integers
    Posted in the Statistics Forum
    Replies: 4
    Last Post: Jul 26th 2008, 04:45 PM

/mathhelpforum @mathhelpforum