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Problem, i went wrong somewhere

  1. Jan 10, 2007 #1
    im stuck on this problem, which is annoying because it looks straightforward, i think i just made a clanger somewhere and cant find where lol, hope ya can help... thnx

    1. The problem statement, all variables and given/known data

    Five clever newsboys formed a partnership and disposed of their papers in the following manner. Tom Smith sold one paper more than one quarter of the whole lot, Billy Jones disposed of one paper more than a quarter of the remainder, Ned Smith sold one paper more than a quarter of what was left, and Charley Jones disposed of one paper more than a quarter of the remainder. At this stage, the Smith boys had together sold just one hundred papers more than the Jones boys had sold. Little Jimmy Jones, the youngest kid in the bunch, now sold all the papers that were left.

    The three Jones boys sold more papers than the two Smith boys, but how many more?

    2. Notation

    Tom Smith = T
    Billy Jones = B
    Ned Smith = N
    Charley Jones = C
    Jimmy Jones = J

    Total number of papers = t

    3. The attempt at a solution

    What I gathered from the problem statement.

    T = 1/4t + 1
    B = 3/16t
    N = 9/64t
    C = 27/256t
    T + N - 100 = B + C
    J = 81/256t - 1

    From that I substituted the letters into T + N - 100 = B + C

    T + N - 100 = B + C
    1/4t + 1 + 9/64t - 100 = 3/16t + 27/256t
    1/4t + 9/64t - 99 = 3/16t + 27/256t
    25/64t - 99 = 75/256t
    25/64t = 75/256t + 99
    25/256t = 99
    t = 1013 19/25 ??

    there cant be a non integer as the no of papers????

    im confused, i think i went wrong at some poitn but cant find where, can anyone help? thnx
  2. jcsd
  3. Jan 10, 2007 #2


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    Science Advisor

    After removing Tom Smiths papers, there were t- (1/4)t- 1= (3/4)t-1 papers left. We are told that "Billy Jones disposed of one paper more than a quarter of the remainder": B= (1/4)((3/4)t-1)+ 1= (3/16)t- 1/4+ 1=
    (3/16)t+ 3/4. You forgot to take 1/4 of the original "one paper less"

    "Ned Smith sold one paper more than a quarter of what was left"
    "What was left" is now (3/4)t- 1- ((3/16)t+ 3/4)= (9/16)t- 7/4. 1/4 of that is (1/4)((9/16)t- 7/4)= (9/64)t- 7/16. "One paper more" is (9/64)t- 7/16+1= (9/64)t+ 9/16.

    Last edited: Jan 10, 2007
  4. Jan 10, 2007 #3
    wait, i think i might know where i went wrong, when turning the quoted sentence into algabra , is it the case that i need to relate it to the number of papers sold so far?

    so should that line look like this?

    T(175/256t + 1) + N(175/256t + 1) - 100 = B(175/256t + 1) + C(175/256t + 1)


  5. Jan 10, 2007 #4
    o rite yeh just saw that reply, thnx buddy
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