Submit ONE copy only to manderso@bcc.ctc.edu, with all group members' names.

Each problem is worth 4 points.

For each problem write (1) the system of equations, (2) the identification of each variable that you used (i.e. describe in ENGLISH what each variables represent) and (3) the solution for each problem. In order to solve each system of equations, use a MATRIX EQUATION AX = B and determine X = A^-1B .

 1. THE DIET. A nutritionist is performing an experiment on student volunteers. He wishes to feed one of his subjects a daily diet that consists of a combination of three commercial diet foods: MiniCal, SloStarve, and SlimQuick. For the experiment it's important that the subject consume exactly 500 mg of potassium, 75 g of protein, and 1150 units of vitamin D every day. The amounts of these nutrients in one ounce of each food are given in the following table.

	MiniCal	SloStarve	SlimQuick
Potassium (mg)	50	75	10
Protein (g)	5	10	3
Vitamin D (units)	90	100	50

How many ounces of each food should the subject eat every day to satisfy the nutrient requirements exactly?

(1) System of equations

(2) Meaning of variables used

(3) Solution

2. MUSICAL PRODUCTION. At a college musical production of Evita , 400 tickets were sold. The ticket prices were $16, $20, and $24, and the total income from ticket sales was $7,400. How many tickets of each type were sold if the combined number of $16 and $20 tickets sold was 7 times the number of $24 tickets sold?

(1) System of equations

(2) Meaning of variables used

(3) Solution

3. A BALANCED BREAKFAST. A study showed that for young women a breakfast containing approximate 23 g protein, 49 g carbohydrate, 20 g fat, and 460 calories is a nutritious breakfast that prevents a hungry feeling before lunch. The following table shows the content of four breakfast foods. How much of each should be served in order to obtain the desired amounts of protein, carbohydrates, fat, and calories?

	PROTEIN	CARBOHYDRATES	FAT	CALORIES
1 cup orange juice	2	24	0	110
1 scrambled egg	8	4	8	120
1 slice bread	2	10	6	100
1 cup skim milk	10	13	0	85

(1) System of equations

(2) Meaning of variables used

(3) Solution

4. INVESTMENT. A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio III consists of 2 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. A customer wants 12 blocks of common stock, 6 municipal bonds, and 6 blocks of preferred stock. How many of each portfolio should be offered?

(1) System of equations

(2) Meaning of variables used

(3) Solution

5. FAST-FOOD FRANCHISE. A fast-food chain sells three types of franchises, A, B, and C. Franchise A sells for $20,000, franchise B for $25,000, and franchise C for $30,000. In one year, the company sold 18 franchises for $430,000. If the number sold of franchise A is twice the number sold of franchise C, how many of each type did the company sell that year?

(1) System of equations

(2) Meaning of variables used

(3) Solution