Results 1 to 5 of 5
Like Tree2Thanks
  • 1 Post By Soroban
  • 1 Post By emakarov

Math Help - Looking for an appropriate algebraic equation for this problem

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    Forest, VA
    Posts
    13

    Looking for an appropriate algebraic equation for this problem

    Problem: In a town, two thirds of the males are married, and three fifths of the females are married. (Marriage between a man and woman) What fraction of the people (male and female) in the town is married?

    Let P = population
    M = males; F= females
    Obviously M+F = P

    Setting an equality, I get:
    2/3*M + 3/5*F = P – (1/3*M + 2/5*F)
    By using the LCD (15):
    10M + 9F = 15P- (5M + 6F)
    Collecting terms and simplifying gives back the original M+F = P

    Intuitively it seems that:
    2/3M + 3/5F would provide the fraction or per cent of the town’s married people.
    P

    Assuming this is correct, is there a better equation that relates more directly to the fraction of the town’s population that is married?

    By substituting arbitrary numerical values for each of the variables, I obtain ~ 0.63 or 63/100 of the town being married. But is their a more appropriate way of algebraically stating this?
    Any help will be appreciated.
    Last edited by jimdec23; June 11th 2012 at 09:05 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,861
    Thanks
    742

    Re: Looking for an appropriate algebraic equation for this problem

    Hello, jimdec23!

    In a town, two thirds of the males are married, and three fifths of the females are married.
    (Marriage between a man and woman.)
    What fraction of the people (male and female) in the town is married?

    I assume that the married men and women are married to each other.
    That is: .(Married men) = (Married women).

    Let . \begin{Bmatrix}M &=& \text{no. of men} \\ W &=& \text{no. women} \end{Bmatrix}

    We are told: . \tfrac{2}{3}M \,=\,\tfrac{3}{5}W \quad\Rightarrow\quad W \,=\,\tfrac{10}{9}M [1]

    The ratio is: . R \;=\;\frac{\text{married men}}{\text{men + women}} \;=\;\frac{\frac{2}{3}M}{M + W}

    Substitute [1]: . R \;=\;\frac{\frac{2}{3}M}{M + \frac{10}{9}M} \;=\;\frac{\frac{2}{3}M}{\frac{19}{9}M} \;=\; \frac{6}{19}
    Thanks from jimdec23
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Looking for an appropriate algebraic equation for this problem

    Assuming there are no people in the town whose spouses live out of town, we have (2/3)M = (3/5)F. This allows expressing M through F. Therefore, the total population M + F can be expressed only through F. Next, the number of married people is twice the number of married females, i.e., 2(3/5)F. When this is divided by the total population expressed through F, the number F is canceled. The final answer I get is 12 / 19.
    Thanks from jimdec23
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2012
    From
    Forest, VA
    Posts
    13

    Re: Looking for an appropriate algebraic equation for this problem

    So, the ratio is expressed as the ratio of married men to the total population. We would then multiply by 2 (to account for the women) to get 12/19 as the faction of all married people in the population. am I correct?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Looking for an appropriate algebraic equation for this problem

    Quote Originally Posted by jimdec23 View Post
    So, the ratio is expressed as the ratio of married men to the total population. We would then multiply by 2 (to account for the women) to get 12/19 as the faction of all married people in the population. am I correct?
    I think so. The question asks for the "fraction of the people (male and female)" who are married, so we need to divide the number of all married people by the total population.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 29th 2012, 04:14 PM
  2. algebraic equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 18th 2011, 09:50 PM
  3. problem with a differential algebraic equation system
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: June 28th 2010, 06:20 PM
  4. algebraic equation problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 30th 2009, 07:11 AM
  5. Algebraic equation for word problem?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 30th 2008, 11:04 PM

Search Tags


/mathhelpforum @mathhelpforum