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**xsolutionx** 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.