X 90 Y 140 Z 210 Lefthand Side Righthand Side 44X 22Y 64Z 20480 20480 20480 42X

X 90 y 140 z 210 lefthand side righthand side 44x 22y

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X 90 Y 140 Z 210 Lefthand Side Righthand Side 44X + 22Y + 64Z = 20480 20480 20480 42X + 28Y + 62Z = 20720 20720 20720 42X + 30Y + 60Z = 20580 20580 20580 Example: An investor owns a portfolio of three stocks: X, Y, and Z. On March 1, the closin prices were X, $44; Y, $22; and Z, $64 per share and the value of the investor's portfolio wa $20,480. Three weeks later, the closing prices were X, $42; Y, $28; and Z, $62 per share an the value of the investor's portfolio was $20,720. Two weeks later, the closing prices were $42; Y, $30; and Z, $60 per share and the value of the investor's portfolio was $20,580. Ho many shares of each stock does the investor hold in the portfolio? Variables: Let X = the number of shares of stock X Let Y = the number of shares of stock Y Let Z = the number of shares of stock Z System of equations: 44X + 22Y + 64Z = 20480 <---Initial value 42X + 28Y + 62Z = 20720 <---Three weeks later 42X + 30Y + 60Z = 20580 <---Two weeks later Therefore, the investor owns 90 shares of Stock X, 140 shares of Stock Y, and 210 shares o Stock Z in the portfolio.
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Department 1-Person Boat 2-Person Boat 4-Peson Boat Cutting 0.5 hr 1.0 hr 1.5 hr Assembly 0.6 hr 0.9 hr 1.2 hr Packaging 0.2 hr 0.3 hr 0.5 hr Cutting 0.5o + 1.0t + 1.5f = 380 Assembly 0.6o + 0.9 t + 1.2f = 330 Packaging 0.2o + 0.3t + 0.5f = 120 Variables o 20 t 220 f 100 Lefthand side Righthand side 0.5o + 1.0t + 1.5f = 380 380 380 0.6o + 0.9 t + 1.2f = 330 330 330 0.2o + 0.3t + 0.5f = 120 120 120 Problem 1: A small manufacturing plant makes three types of inflatable boats: one-person, two-person, and four-person models. The construction of each boat requires the services of three departments, as listed below in the table. The cutting, assembly, and packaging departments have a maximum of 380, 330, and 120 labor-hours available per week, respectively. How many boats of each type must be manufactured each week for the plant to operate at full capacity? Variables: Let o = the number of one-person boats Let t = the number of two -person boats Let f = the number of four -person boats System of equations: Summary : Tmanufacturing plant must make 20 one-person boats, 220 two-person boats, and 100 four-person boats per week to operate at full capacity.
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Food A Food B Food C Calcium 30 10 20 Iron 10 10 20 Vitamin A 10 30 20 Systems of equations: Calcium 30A + 10B + 20C = 340 Iron 10A + 10B + 20C = 180 Vitamin A 10A + 30B + 20C = 220 Variables A 8 B 2 C 4 Lefthand sideRighthand side 30A + 10B + 20C = 340 340 340 10A + 10B + 20C = 180 180 180 10A + 30B + 20C = 220 220 220 Problem 2: A dietician in a hospital is to arrange a special diet composed of three basic foods. The diet is to include exactly 340 units of calcium, 180 units of iron, and 220 units of vitamin A. The number of units per ounce of each special ingredient for each of the foods is listed int he table below. How many ounces of each food must be used to meet the diet requirements? Variables: Let A = the number of ounces of Food A Let B = the number of ounces of Food B Let C = the number of ounces of Food C Summary: The dietician has to use 8 ounces of Food A, 2 ounces of Food B, and 4 ounces of Food C to meet the diet requirements.
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Systems of equations: Phosphoric Acid 30A + 30B + 30C + 60D=900 Nitrogen 50A + 75B + 25C +25D = 750 Potash 30A + 20B + 20C + 50D = 700 Variables A 0 B 5 C 5 D 10 Lefthand sideRighthand side 30A + 30B + 30C + 60D=900 900 900 50A + 75B + 25C +25D = 750 750 750 30A + 20B + 20C + 50D = 700 700 700 Problem 3: A farmer can buy four types of plant food.
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