Results 1 to 12 of 12

Math Help - how many ways to make change for 100 dollars?

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    175

    how many ways to make change for 100 dollars?

    using 10 and 20 dollar bills?

    its a generating function problem, for the life of me i dont know what to do.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    The answer is the coefficient of x^{100} in the expansion of \left( {\sum\limits_{k = 0}^{10} {x^{10k} } } \right)\left( {\sum\limits_{k = 0}^5 {x^{20k} } } \right).

    Can you finish?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hallo !

    Quote Originally Posted by Plato View Post
    The answer is the coefficient of x^{100} in the expansion of \left( {\sum\limits_{k = 0}^{10} {x^{10k} } } \right)\left( {\sum\limits_{k = 0}^5 {x^{20k} } } \right).

    Can you finish?
    How do you get it ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by Moo View Post
    How do you get it ?
    Why not allow p00ndawg to answer that question you us?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by Plato View Post
    Why not allow p00ndawg to answer that question you us?
    Let's wait for it then
    Or if you could provide a starting of answer by PM...if it doesn't bother you :x
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Feb 2008
    From
    Westwood, Los Angeles, CA
    Posts
    176
    Thanks
    1
    Quote Originally Posted by p00ndawg View Post
    using 10 and 20 dollar bills?

    its a generating function problem, for the life of me i dont know what to do.
    Maybe this isn't really the way you're supposed to do it, but can't we just reason that, when making change for $100, we can use either 0, 1, 2, 3, 4, or 5 $20 bills, with the rest being $10 bills, so there are 6 ways?

    (Specifically, for ($10, $20): (10, 0), (8, 1), (6, 2), (4, 3), (2, 4), and (0, 5))
    Last edited by Mathnasium; May 8th 2008 at 09:05 AM. Reason: Corrected last ordered pair; obvious typo, no rethinking required.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by Mathnasium View Post
    Maybe this isn't really the way you're supposed to do it, but can't we just reason that, when making change for $100, we can use either 0, 1, 2, 3, 4, or 5 $20 bills, with the rest being $10 bills, so there are 6 ways?

    (Specifically, for ($10, $20): (10, 0), (8, 1), (6, 2), (4, 3), (2, 4), and (1, 5))
    Rethink that (1 ; 5) one. (Equals $110)
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Jan 2008
    Posts
    175
    Quote Originally Posted by Mathnasium View Post
    Maybe this isn't really the way you're supposed to do it, but can't we just reason that, when making change for $100, we can use either 0, 1, 2, 3, 4, or 5 $20 bills, with the rest being $10 bills, so there are 6 ways?

    (Specifically, for ($10, $20): (10, 0), (8, 1), (6, 2), (4, 3), (2, 4), and (0, 5))
    thanks for all the help, this question was actually on my final and I ended up doing what you say. Because when I took the test earlier this morning i just couldnt figure out any other way to do it.

    but i just wanted to actually know the mathematical way to do it.


    Mr. plato gave the way im assuming my teacher wanted it, but I totally did not expect that question, I think the answer I got was right (6), but im not sure if he'll approve of my methods lol.

    So i think i may have gotten it right.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by p00ndawg View Post
    thanks for all the help, this question was actually on my final and I ended up doing what you suggested.

    but i just wanted to actually know the mathematical way to do it.


    Mr. plato gave the way im assuming my teacher wanted it, but I totally did not expect that question, I think the answer I got was right (6), but im not sure if he'll approve of my methods lol.

    So i think i may have gotten it right.
    Your final?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member
    Joined
    Jan 2008
    Posts
    175
    Quote Originally Posted by janvdl View Post
    Your final?
    Yea it was on my final, I just wanted to see how to do it. After I took the test that was really the only problem that bugged me.

    now I just got to read up on cal 2 for tomorrow.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by p00ndawg View Post
    the way im assuming my teacher wanted it, but I totally did not expect that question, I think the answer I got was right (6), but im not sure if he'll approve of my methods.
    It could be that the instructor expected the exact answer the way I gave it.
    I have asked students to set up such problems just to check on understanding.
    Unless one spends a good deal of time on how coefficients are calculated from generating functions, I donít think we can expect much more than that. There is in fact a whole textbook on generating functions, it could be a whole course.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member
    Joined
    Jan 2008
    Posts
    175
    Quote Originally Posted by Plato View Post
    It could be that the instructor expected the exact answer the way I gave it.
    I have asked students to set up such problems just to check on understanding.
    Unless one spends a good deal of time on how coefficients are calculated from generating functions, I donít think we can expect much more than that. There is in fact a whole textbook on generating functions, it could be a whole course.
    yea he might have, and I did indeed go through the whole coefficient process of figuring it out. He's is kind of lenient at times, and im hoping he'll give it to me because the test was fairly rough.

    There was one other curveball question he put on the test that I didnt even THINK of reviewing, my fault of course, I couldnt even start the problem lol.

    Anyways thanks for the quick reply.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to make a change of basis?
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 5th 2011, 11:50 AM
  2. Replies: 1
    Last Post: January 8th 2011, 09:55 AM
  3. number of ways to make team
    Posted in the Statistics Forum
    Replies: 3
    Last Post: December 4th 2008, 03:23 AM
  4. Please help, ill paypal you 5 dollars if its right.
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: September 10th 2005, 07:26 PM

Search Tags


/mathhelpforum @mathhelpforum