Results 1 to 9 of 9

Math Help - worded problems

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    21

    worded problems

    Can someone help me put this into equations and solve them:

    1. Phil has $150 and three-quarters of what Jill has, and Jill has $100 and half of what Phil has, so how much have each?

    2. If a teacher can place her students four to a table, there will be three students on the final table. But, if five children are placed on each table, there will be four students on the the last table.

    What is the smallest number of children the class could have?


    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Stroodle's Avatar
    Joined
    Jun 2009
    Posts
    367
    For the first one let Phil's money be P and Jill's money be J

    The two equations you get from this information are:

    P=150+\frac{3}{4}J

    and

    J=100+\frac{1}{2}P

    Solve these equations simultaneously to get the solutions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    21
    Hi,

    Thanks for the reply. I got up to that stage. I guess my problem is solving the equation.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member Stroodle's Avatar
    Joined
    Jun 2009
    Posts
    367
    Oh,

    If you plug the second equation into the first one you get:

    P=150+\frac{3}{4}\left (100+\frac{1}{2}P\right )

    4P=600+3\left (100+\frac{1}{2}P\right ) (multiplied everything by 4)

    4P=600+300+\frac{3}{2}P

    8P=1200+600+3P (multiplied everything by 2)

    5P=1800

    P=360

    Now if you plug this value of P into one of the first two equations you'll also get the solution for J
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    21
    Ah, thanks.


    How do you determine to multiply by 8 and 4? To bring the fractions to integers?

    I was trying with substitution, but when multiplying out the first line (before multiply x 8) I would get the wrong answer. As a side question, why doesn't that work?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member Stroodle's Avatar
    Joined
    Jun 2009
    Posts
    367
    To clear the fractions you just multiply the equation by the denominator of the fraction in question.
    As far as I'm aware the method I used is called substitution, but if you post your working here we can try to see where you went wrong.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2009
    Posts
    21
    I was attempting to do it this way:

    (sorry couldn't get the math code to work)

    p = 150 + 3/4 (100 + 1/2p )

    p = 150 + 75 + 3/8P

    P = 225 + 3/8p

    225 = 5/8p

    p = 309.37
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member Stroodle's Avatar
    Joined
    Jun 2009
    Posts
    367
    Your method is correct, except for the last step.

    \frac{5P}{8}=225

    \therefore 5P=1800

    \therefore P=360
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Nov 2009
    Posts
    21
    Damn, so simple.

    cheers for the help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Worded question.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 26th 2011, 11:54 PM
  2. Worded problems (difference equations)
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 24th 2010, 03:00 AM
  3. Replies: 5
    Last Post: September 12th 2009, 08:42 PM
  4. Replies: 2
    Last Post: September 12th 2009, 08:08 PM
  5. Worded problems.
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 23rd 2008, 09:47 PM

Search Tags


/mathhelpforum @mathhelpforum