Results 1 to 4 of 4

Math Help - Algebraic ways of solving these problems.

  1. #1
    Newbie
    Joined
    Mar 2006
    Posts
    2

    Algebraic ways of solving these problems.

    Im taking a simple introductory arithmetic math course in Uni and the professor I have is using bizarre methods to solve seemingly simple world problems. I would like to solve this problems algebraically as Im most comfortable using this method, only problem is that I have forgotten the ways to solve these word problems.

    Any help is greatly appreciated.

    E.g
    1.
    A team of 15 employees, working 6 hours a day, does a job in 9 days. How many employees, working 9 hours a day, would be needed to do the same job in 5 days?

    2.
    A mixture of 100kg of tea at $20 per kg is made up of 60kg at $22 per kg and 40kg at a certain price. What is the price per kg of the second tea?

    3.
    In what proportion should one mix flour at $1.2 per kg with flour at $1.6 per kg to obtain a mixture at $1.35 per kg?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by adriano1028
    A team of 15 employees, working 6 hours a day, does a job in 9 days. How many employees, working 9 hours a day, would be needed to do the same job in 5 days?
    That means,
    15 Employees|6 hours|9 days.
    Thus, 1 Employee need to work for 90 hours a day, Thus,
    1 Employee|90 hours|9 days.
    Thus, working for 1 hour he needs 9x90=810 days, Thus,
    1 Employee|1 hour| 810 days.
    This to do the same amount of work, 1 employee working for 1 hour needs 810 days.
    --------
    We need to find
    X Employees|9 hours|5 days
    Thus, 1 Employee needs to work for 9X hours a day, Thus,
    1 Employee|9X hours|5 days
    Thus, working for 1 hours he needs 45X hours a day, Thus,
    1 Employee|1 hour|45X days.
    This to do the same amount of work, 1 employee working for 1 hour needs 45X days.
    --------
    Before we show it is 810 days, thus,
    45X=810 days,
    Thus,
    X=18 Employees.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123

    tea-time

    Quote Originally Posted by adriano1028
    ...

    2.
    A mixture of 100kg of tea at $20 per kg is made up of 60kg at $22 per kg and 40kg at a certain price. What is the price per kg of the second tea?
    Hello,

    let the price be x.
    Then calculate the value of your tea-mixture:
    100 kg \cdot 20 \frac{\$}{kg}= 60 kg \cdot 22 \frac{\$}{kg}+40 kg \cdot x

    Solve this equation for x und you'll get: x = 17 $/kg

    Greetings

    EB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123

    flour power

    Quote Originally Posted by adriano1028
    ...
    3.
    In what proportion should one mix flour at $1.2 per kg with flour at $1.6 per kg to obtain a mixture at $1.35 per kg?
    Hello,

    let us suppose, that you want to produce exactly 1 kg of the flour-mixture. The ingredients are x kg of the cheaper flour and (1-x) kg of the more expensive one. Translate this sentence into an equation:
    x \cdot 1.2 \frac{\$}{kg}+(1-x) \cdot 1.6 \frac{\$}{kg}= 1 kg \cdot 1.35 \frac{\$}{kg}

    Solve this equation for x and you'll get: x = 0.625 kg of the cheap flour
    and 0.375 kg of the expensive flour.

    It is asked for the proportion so you'll get:
    \frac{expensive}{cheap}=\frac{.375}{.625}=\frac{3}  {5}

    Greetings

    EB
    Last edited by earboth; March 23rd 2006 at 07:25 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. I have problems with algebraic fractions.
    Posted in the Algebra Forum
    Replies: 7
    Last Post: August 12th 2010, 04:47 AM
  2. algebraic word problems
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 5th 2010, 03:37 AM
  3. Replies: 1
    Last Post: July 9th 2009, 07:44 PM
  4. Ways of solving quadratic relations
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: December 15th 2008, 07:37 PM
  5. need help with these two algebraic problems
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 11th 2008, 05:21 PM

Search Tags


/mathhelpforum @mathhelpforum