Results 1 to 2 of 2

Math Help - Critical Thinking System of 3 Equations Problem

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    1

    Post Critical Thinking System of 3 Equations Problem

    Abe gives Rafer as many raffle tickets as Rafer already had and Jorge as many as Jorge already had. Then Rafer gives Abe and Jorge as many tickets as each of them has. Similarly, Jorge gives Abe and Rafer as many tickets as each of them has. They each end up with 40 tickets. How many tickets did Rafer have at the beginning?

    I know Abe, Jorge, and Rafer all have 40 which gives me 120. But now I'm trying to work backwards or create equations. Please help and explain.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123

    Re: Critical Thinking System of 3 Equations Problem

    Quote Originally Posted by petey615 View Post
    Abe gives Rafer as many raffle tickets as Rafer already had and Jorge as many as Jorge already had. Then Rafer gives Abe and Jorge as many tickets as each of them has. Similarly, Jorge gives Abe and Rafer as many tickets as each of them has. They each end up with 40 tickets. How many tickets did Rafer have at the beginning?

    I know Abe, Jorge, and Rafer all have 40 which gives me 120. But now I'm trying to work backwards or create equations. Please help and explain.
    I would use a table:

    1. Let a, r, j denote the number of tickets of Abe, Rafer and Jorge.

    2. Then they have:
    \begin{array}{ccccccc}\text{step}&|&\text{Abe} &|& \text{Rafer} &|& \text{Jorge} \\ <br />
0&|& a &|& r &|&  j \\<br />
1 &|&  a-r-j &|& 2r &|&  2j \\ <br />
2 &|&  2(a-r-j) &|& 2r-(a-r-j)-2j &|&  4j \\ <br />
3 &|&  4(a-r-j) &|& 2(3r-a-j) &|&  4j-2(a-r-j)-(3r-a-j) \\ <br />
\end{array}

    3. The terms in the last line have the value 40. That means you have a system of 3 simultaneous equations.
    Spoiler:
    I've got (a,r,j)=(65, 35, 20)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Critical Thinking with Functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: August 22nd 2011, 01:51 AM
  2. System of equations problem
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 23rd 2009, 02:50 PM
  3. Critical Thinking
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 20th 2007, 10:43 PM
  4. critical thinking vectors
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: January 7th 2007, 11:24 AM
  5. critical thinking trig problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 6th 2007, 12:54 PM

Search Tags


/mathhelpforum @mathhelpforum