Results 1 to 8 of 8

Math Help - Substitution Word Problem

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    6

    Substitution Word Problem

    I'm fine with regular substitution problems, but this word problem is really bothering me:


    A writing workshop enrolls novelists and poets in a ratio of 5 to 3. There are 24 people at the workshop. How many novelists are there? How many poets are there?

    I've tried to write down some equations, but they were all wrong. Does n + p = 24?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    NRS
    NRS is offline
    Newbie NRS's Avatar
    Joined
    Feb 2010
    Posts
    18
    n + p = 24 is correct.

    to get the others:

    (3/5)n = p

    (5/3)p = n
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by JayRich88 View Post
    I'm fine with regular substitution problems, but this word problem is really bothering me:


    A writing workshop enrolls novelists and poets in a ratio of 5 to 3. There are 24 people at the workshop. How many novelists are there? How many poets are there?

    I've tried to write down some equations, but they were all wrong. Does n + p = 24?
    Hi JayRich88,

    Here's another way to look at this.

    The ratio of the number of Novelists (N) to the number of Poets (P) is \frac{N}{P}=\frac{5}{3}

    The Total (T) in this is 5 + 3 = 8 Novelists and Poets.

    Now set up a couple of proportions where Total (T) goes from 8 to 24:

    [1] \frac{N}{T}\Longrightarrow\frac{5}{8}=\frac{N}{24}

    [2] \frac{P}{T}\Longrightarrow\frac{3}{8}=\frac{P}{24}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, JayRich88!

    Yet another way . . . (not too different).


    A writing workshop enrolls Novelists and Poets in a ratio of 5 to 3.
    There are 24 people at the workshop.
    How many novelists are there? How many poets are there?

    I've tried to write down some equations, but they were all wrong.

    Does N + P \:=\: 24 ? . . Yes!
    Use the "ratio" information.

    We are told: . N:P \:=\:5:3 \quad\Rightarrow\quad \frac{N}{P} \:=\:\frac{5}{3} \quad\Rightarrow\quad N \:=\:\frac{5}{3}P

    Now substitute that into your equation.


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Another approach to Ratio problems . . .

    Let 5n = number of Novelists.
    Let 3n = number of Poets.

    Then: . 5n+3n \:=\:24 \quad\Rightarrow\quad n = 3

    Therefore: . \begin{Bmatrix}5n &=&15 & \text{ Novelists} \\ 3n &=& 9 & \text{ Poets} \end{Bmatrix}

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2010
    Posts
    6
    Thank you all. I knew that there would be 15 novelists and 9 poets! I just didn't know I would use only one variable! Thanks
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Feb 2010
    Posts
    6
    Just so I could get a better understanding, may someone explain the fact that N= 5/3P?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by JayRich88 View Post
    Just so I could get a better understanding, may someone explain the fact that N= 5/3P?
    Sure, JayRich88.

    \frac{N}{P}=\frac{5}{3}, right?

    Now, just use the cross product rule to get:

    3N=5P

    Finally, divide both sides by 3 and you get:

    N=\frac{5}{3}P
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Feb 2010
    Posts
    6
    Ah, I see! Thanks very much.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. elimination and substitution word problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 3rd 2008, 09:23 AM
  2. Need help with a u-substitution problem
    Posted in the Calculus Forum
    Replies: 12
    Last Post: September 23rd 2008, 06:09 PM
  3. Substitution word problem
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: January 21st 2008, 07:35 PM
  4. Substitution word problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 21st 2008, 06:19 PM
  5. [SOLVED] [SOLVED] Word Problem - Solve by Substitution
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 3rd 2005, 10:19 PM

Search Tags


/mathhelpforum @mathhelpforum