Results 1 to 3 of 3

Math Help - Cramers rule and equations help

  1. #1
    Newbie
    Joined
    Dec 2007
    Posts
    7

    Cramers rule and equations help

    hi guys i'm having some problem finding the correct 3 equations which go with the each of these problems. i know how to work it through cramer's rule already if you can help me out that would be great!

    1. A company invests a total of $1 million in three different forms: short-term loans, treasury notes, and municipal bonds. The short-term loans pay annual interest at a rate of 10%, the treasury notes pay 8% interest, and the bonds pay 4% interest. The total interest for the year is $60,000 or $0.06 million. If the company has three times as much money invested in municipal bonds as in treasury notes, how much money is invested in each type of investment?

    2. The annual report of a company contains a summary of personnel figures. It states that the company has a total of 900 employees in three classifications-clerical, factory, and trainee- and that it budgets a total of 2450 weeks for paid vacations for these employees during the year and 10, 450 days for paid sick leave. The report also states that a clerical employee receives 2 weeks of paid vacation and 8 days of sick leave each year, that a factory employee receives 3 weeks of vacation and 13 days of sick leave, and that a trainee gets 1 week of vacation and 3 days of sick leave. The report does not state how many employees the company has in each of the three categories. If possible, determine this from the information given.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by xsolutionx View Post
    1. A company invests a total of $1 million in three different forms: short-term loans, treasury notes, and municipal bonds. The short-term loans pay annual interest at a rate of 10%, the treasury notes pay 8% interest, and the bonds pay 4% interest. The total interest for the year is $60,000 or $0.06 million. If the company has three times as much money invested in municipal bonds as in treasury notes, how much money is invested in each type of investment?
    Ok, let's take this step by step:

    Let x be the amount of money invested in loans
    Let n be the amount of money invested in notes
    Let b be the amount of money invested in bonds

    Since the company invests a total of $1 million, we have:

    x + n + b = 1

    Since the short-term loans pay annual interest at a rate of 10%, the treasury notes pay 8% interest, and the bonds pay 4% interest, and the total interest for the year is $0.06 million, we have:

    0.1x + 0.08n + 0.04b = 0.06

    Since, the company has three times as much money invested in municipal bonds as in treasury notes, we have:

    b = 3n

    or

    b - 3n = 0

    Thus, we need to solve the system:

    \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0.1 & 0.08 & 0.04 \\ 0 & -3 & 1 \end{array} \right) \left( \begin{array}{c} x \\ n \\ b \end{array} \right) = \left( \begin{array}{c} 1 \\ 0.06 \\ 0 \end{array} \right)

    Can you use this reasoning to set up the system for the second?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2007
    Posts
    7
    Quote Originally Posted by Jhevon View Post
    Ok, let's take this step by step:

    Let x be the amount of money invested in loans
    Let n be the amount of money invested in notes
    Let b be the amount of money invested in bonds

    Since the company invests a total of $1 million, we have:

    x + n + b = 1

    Since the short-term loans pay annual interest at a rate of 10%, the treasury notes pay 8% interest, and the bonds pay 4% interest, and the total interest for the year is $0.06 million, we have:

    0.1x + 0.08n + 0.04b = 0.06

    Since, the company has three times as much money invested in municipal bonds as in treasury notes, we have:

    b = 3n

    or

    b - 3n = 0

    Thus, we need to solve the system:

    \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0.1 & 0.08 & 0.04 \\ 0 & -3 & 1 \end{array} \right) \left( \begin{array}{c} x \\ n \\ b \end{array} \right) = \left( \begin{array}{c} 1 \\ 0.06 \\ 0 \end{array} \right)

    Can you use this reasoning to set up the system for the second?
    yes thank you very much! i appreciate all your guys' help tonight.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. cramers rule problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: December 13th 2010, 06:20 PM
  2. help please word problem with cramers rule
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 13th 2010, 06:19 PM
  3. Replies: 2
    Last Post: December 9th 2010, 05:38 PM
  4. question about cramers rule
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 18th 2010, 06:48 AM
  5. Help solving/ understanding (Cramers Rule)
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 17th 2007, 07:14 PM

Search Tags


/mathhelpforum @mathhelpforum