Instructions:
For each problem the student must figure out the system of equations given by the problem.
Once they have gotten the system, open up Graphing Calculator and enter those equations into the program and graph them. From the graph answer the problem.
After answering the problem graphically, the students should make a matrix out of the equations. Using their calculators (TI-83, TI-83 plus, or TI-84 plus) put the matrix into the calculator and perform a reduced row echelon procedure to get a solution to the equations.
Compare the graphical solutions with the matrix solutions.
Problems:
1. Sam is in charge of ordering the plaques for a school awards banquet. There are three type, which cost $21, $38, and $50. He needs to order some of each for a total of 26 plaques and a total cost of $1030. He needs 2 fewer of the $21 plaques than of the $38 plaques. How many of each plaque does he need to order?
2. Black Forest Bakery sells three kinds of muffin: chocolate chip muffins at $0.50 each, oatmeal muffins at $0.55 each, and cranberry muffins at $0.60 each. Tim buys some of each kind and chooses three time as many cranberry muffins as chocolate chip muffins. If he spends $11.95 on 21 muffins, how many of each type of muffin did he buy?
3. Sally has three investments totaling $100,000. These investments earn interest at 8%, 10%, and 12% respectively. Sally's total income from these investements is $10,800. The income from the 12% investment exceeds the total income from the other two investments by $1200. Find how much Sally has in each of the three investments.
4. A landscaper is hired to consruct a garden in front of a business complex. the complex owners would like the garden to resemble their logo, which is a triangle with specific angle measures. The middle-sized andle measures 12 degreea more than 2 times the smallest angle. the middle-sized andle measures 56 degrees less than the largest angle. Find the measure of each angle of the triangular garden that the landscaper must construct.
This last problem is using inequalities, thus cannot be done in matrix form. Still use Graphing Calculator to come up with the solution. (Hint: look at the points of intersection)
5. Roland's Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 8 economy seats must be sold and at least 5 deluxe seats must be sold. The maximum number of passengers allowed on each boat is 45. Roland's Boat Tours makes $35 profit for each economy seat sold and $30 profit for each deluxe seat sold. What is the maximum profit from one tour?