Results 1 to 2 of 2

Thread: Random question

  1. #1
    Junior Member
    Joined
    Dec 2007
    Posts
    41

    Random question

    from the Australian Intermediate Mathematics Olympiad:

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, delicate_tears!


    Let $\displaystyle S,\,T\,,F$ = number of 6-, 10-, and 15-passenger taxis, respectively,
    . . where: .$\displaystyle S,\,T,\,F\:\leq\:6$

    We have: .$\displaystyle 6S + 10T + 15F \:=\:120$

    . . Hence: .$\displaystyle F \:=\:\frac{120-6S - 10T}{15} \quad\Rightarrow\quad F \:=\;8\; -\; \frac{2S}{5}\;-\; \frac{2T}{3}$ .[1]


    Since $\displaystyle F$ is an integer, .$\displaystyle \begin{array}{cc}S\text{ is a multiple of 5:} & S = 5h \\ T\text{ is a multiple of 3:} & T = 3k \end{array}$

    . . Then [1] becomes: .$\displaystyle F \;=\;8 - 2h - 2k \;=\;8 - 2(h + k)$


    Since $\displaystyle S,\,T\:\leq\:6$, then: .$\displaystyle h \:=\:0,1\text{ and }k \:=\:0,1,2$


    It seems that there are: .$\displaystyle 2 \times 3 \:=\:6$ possible choices.

    However, if $\displaystyle h = k = 0$, then $\displaystyle F = 8$ . . . not allowed.


    Therefore, there are $\displaystyle \bf{\color{blue}5}$ ways.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability and random random varible question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 15th 2010, 08:53 PM
  2. Random Calculus Question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Apr 24th 2009, 11:46 PM
  3. random big o question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Mar 5th 2009, 10:28 AM
  4. Functions and a random question
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Nov 13th 2008, 03:06 PM
  5. Random Question.... :P
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: Oct 1st 2008, 09:01 PM

Search Tags


/mathhelpforum @mathhelpforum