Results 1 to 5 of 5
Like Tree3Thanks
  • 2 Post By romsek
  • 1 Post By SlipEternal

Math Help - prove using induction...

  1. #1
    Member
    Joined
    Jun 2014
    From
    In ah House
    Posts
    75
    Thanks
    2

    prove using induction...

    Prove by induction : show that $24 or more can be dispensed from an ATM using only $5 and $7 notes.

    how do i go about doing this?
    Last edited by mathman11; July 7th 2014 at 01:04 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,789
    Thanks
    1149

    Re: prove using induction...

    Quote Originally Posted by mathman11 View Post
    Prove by induction : show that \$24 or more can be dispensed from an ATM using only \$5 and \$7 notes.

    how do i go about doing this?
    reposted fixing \$'s
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,789
    Thanks
    1149

    Re: prove using induction...

    Quote Originally Posted by mathman11 View Post
    Prove by induction : show that \$24 or more can be dispensed from an ATM using only \$5 and \$7 notes.

    how do i go about doing this?
    1st can you do this with \$24?

    $2\times 5 + 2 \times 7 = 24$, so yes you can.

    Suppose you can do it with \$D. Show you can do it with \$(D+1).

    $D = 5m+7k,~~m,k \in \mathbb{N}$

    $D+1 = 5m + 7k + 1 = \dots$

    you should be able to finish from here.

    There are a couple different ways of obtaining D+1 and you'll need to use both of them.
    Last edited by romsek; July 7th 2014 at 01:37 PM.
    Thanks from HallsofIvy and topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jun 2014
    From
    In ah House
    Posts
    75
    Thanks
    2

    Re: prove using induction...

    kool this helped!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,937
    Thanks
    785

    Re: prove using induction...

    I would use five base cases:
    24 = 2\times 5 + 2\times 7
    25 = 5\times 5+ 0 \times 7
    26 = 1\times 5 + 3\times 7
    27 = 4\times 5 + 1\times 7
    28 = 0\times 5 + 4\times 7

    For any n\ge 24, you can write n=5k+24, n=5k+25, n=5k+26, n=5k+27,\text{ or }n=5k+28 for some nonnegative integer k. It can only be written as one of them. Depending on how it can be written, you use the appropriate breakdown of the base number, then add k $\$5$ notes.
    Thanks from mathman11
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. how do you prove this using induction
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 23rd 2014, 09:18 AM
  2. Prove using induction
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: August 13th 2011, 10:07 AM
  3. Replies: 10
    Last Post: June 29th 2010, 01:10 PM
  4. Induction to prove
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: August 27th 2009, 05:19 AM
  5. need help with induction prove..
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 16th 2008, 10:13 AM

Search Tags


/mathhelpforum @mathhelpforum