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Math Help - Cramer's Rule Help

  1. #1
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    Cramer's Rule Help

    hey guys i was given some questions a while ago by my instructor for extra credit but i cant seem to figure these out correctly. I figure maybe one of you guys can help me get my much needed extra points so i can hopefully pass this semester. thanks a ton in advance!

    What i need:
    1. inital 3 equations
    2. list what the three letters are representing.
    3. a modified 3x3 matrix
    4. cramer's rule applied to each variable



    Example 1:
    The ABC Shipping Company charges $2.90 for all packages weighing less than or equal to 5 lbs, $5.20 for packages weighting more than 5 lbs and less than 10 lbs, and $8.00 for all packages weighing 10 lbs or more. The number of packages weighing 5 lbs or less is 50% more than the number of packages weighing 10 lbs or more. One day shipping charges for 300 orders was $1,508. Find the number of packages in each category.


    Example 2:
    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?


    Problem 3:
    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.
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  2. #2
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    if i can even just get the initial 3 equations for each i can try and work the problems out and get some partial points.
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  3. #3
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    Quote Originally Posted by xsolutionx View Post
    hey guys i was given some questions a while ago by my instructor for extra credit but i cant seem to figure these out correctly. I figure maybe one of you guys can help me get my much needed extra points so i can hopefully pass this semester. thanks a ton in advance!

    What i need:
    1. inital 3 equations
    2. list what the three letters are representing.
    3. a modified 3x3 matrix
    4. cramer's rule applied to each variable



    Example 1:
    The ABC Shipping Company charges $2.90 for all packages weighing less than or equal to 5 lbs, $5.20 for packages weighting more than 5 lbs and less than 10 lbs, and $8.00 for all packages weighing 10 lbs or more. The number of packages weighing 5 lbs or less is 50% more than the number of packages weighing 10 lbs or more. One day shipping charges for 300 orders was $1,508. Find the number of packages in each category.


    Example 2:
    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?


    Problem 3:
    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.
    Why don't you pick a problem, work it out as best you can, and perhaps we will be able to give you some (general) information that might be helpful.

    -Dan
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