Results 1 to 3 of 3

Math Help - Algebra Help

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    9

    Algebra Help

    Here is part of a working given by an answer of a particular question:

    40*(a–b)=50*(x–y)
    If a, b, x, and y are whole numbers, (a – b) must in fact be a multiple of 5.

    Why must (a-b) a multiple of five?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,957
    Thanks
    1631
    Quote Originally Posted by Lupin View Post
    Here is part of a working given by an answer of a particular question:

    40*(ab)=50*(xy)
    If a, b, x, and y are whole numbers, (a b) must in fact be a multiple of 5.

    Why must (a-b) a multiple of five?
    The first thing you can do is divide both sides by 10: 4(a-b)= 5(x-y). Since 5 is a prime factor on the right, it must also be a factor on the left. 4 obviously has no factor of 5 so a-b must have a factor of 5.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    Quote Originally Posted by Lupin View Post
    40*(ab)=50*(xy)
    If a, b, x, and y are whole numbers, (a b) must in fact be a multiple of 5.

    Why must (a-b) a multiple of five?
    Divide through by 10: 4(a - b) = 5(x - y)

    You know that a, b, x, and y are whole numbers, so, even if the differences give you negatives, a - b and x - y have to be integers (whole numbers or their negatives).

    Dividing through by 5, you get x - y = (4/5)(a - b).

    Since x - y is a whole number (or the negative of a whole number), then (4/5)(a - b) must also be such. You know that 4/5 isn't a whole number. Then there must be something in a - b that "cancels off" with the "5" in the denominator of 4/5, so that (4/5)(a - b) ends up having no denominator.

    The only thing that could cancel off is a factor of 5, so a - b must be factorable, and one of its factors must be 5.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 4th 2011, 08:39 AM
  2. Replies: 2
    Last Post: December 6th 2010, 03:03 PM
  3. Algebra or Algebra 2 Equation Help Please?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 12th 2010, 11:22 AM
  4. Replies: 0
    Last Post: April 23rd 2010, 11:37 PM
  5. algebra 2 help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 4th 2009, 06:24 PM

Search Tags


/mathhelpforum @mathhelpforum