768 CHAPTER 11 Systems of Equations and Inequalities 35 g of carbohydrates, and 200 mg of calcium. Each serving of corn has 3 g of protein, 16 g of carbohydrates, and 10 mg of calcium. Each glass of 2% milk has 9 g of protein, 13 g of carbohydrates, and 300 mg of calcium. How many servings of each food should the dietitian provide for the patient? 82. Investments Sheridan entered a poem-writing competition when she was in eighth grade and won first place with a prize of $2000. As her financial planner, her mom recommends that she diversify in three investments: Treasury bills that yield 5% simple interest, Treasury bonds that yield 7% simple interest, and corporate bonds that yield 10% simple interest. To have enough money for a down payment on a car when she graduates from college, Sheridan has calculated that she will need to earn $139 per year in income. Also, Sheridan wants her investment in Treasury bills to be $300 more than her investment in corporate bonds. How much money should Sheridan place in each investment? 83. Prices of Fast Food One group of customers bought 8 deluxe hamburgers, 6 orders of large fries, and 6 large colas for $26.10. A second group ordered 10 deluxe hamburgers, 6 large fries, and 8 large colas and paid $31.60. Is there sufficient information to determine the price of each food item? If not, construct a table showing the various possibilities.Assume that the hamburgers cost between $1.75 and $2.25, the fries between $0.75 and $1.00, and the colas between $0.60 and $0.90. 84. Prices of Fast Food Use the information given in Problem 83. Suppose that a third group purchased 3 deluxe hamburgers, 2 large fries, and 4 large colas for $10.95. Now is there sufficient information to determine the price of each food item? If so, determine each price. 85. Painting a House Three painters (Beth, Dan, and Edie), working together, can paint the exterior of a home in 10 hours (h). Dan and Edie together have painted a similar house in 15 h. One day, all three worked on this same kind of house for 4 h, after which Edie left. Beth and Dan required 8 more hours to finish. Assuming no gain or loss in efficiency, how long should it take each person to complete such a job alone? 86. Challenge Problem Solve for x and y, assuming ≠ a 0 and ≠ b 0. ax by a b abx b y b ab 2 2 + = + − = − ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ 87. Challenge Problem Solve for x, y, and z, assuming ≠ ≠ a b 0, 0, and ≠ c 0. + + = + + + + = + + + = + ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ ax by cz a b c ax by cz ac ab bc abx bcy bc ac 2 2 2 77. Electricity: Kirchhoff’s Rules An application of Kirchhoff’s Rules to the circuit shown results in the following system of equations: I I I I I I I 5 3 5 0 10 5 7 0 2 1 3 1 2 2 3 = + − − = − − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ Find the currents I I , , 1 2 and I .3 3V 5V I2 I1 I3 7V 10 V 1 2 1 2 5 V Source: Physics for Scientists & Engineers, 9th ed., by Serway. © 2013 Cengage Learning. 78. Electricity: Kirchhoff’s Rules An application of Kirchhoff’s Rules to the circuit shown below results in the following system of equations: I I I I I I I 8 4 6 8 4 6 3 1 2 3 2 1 2 = + = + = + ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ Find the currents I I , , 1 2 and I .3 I2 3V 5V 1V 1V 2 1 4 V 12 V 8V 2 1 I1 I3 Source: Physics for Scientists & Engineers, 9th ed., by Serway. © 2013 Cengage Learning. 79. Theater Revenues A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $150, main seats for $135, and balcony seats for $110. If all the seats are sold, the gross revenue to the theater is $64,250. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $56,750. How many of each kind of seat are there? 80. Theater Revenues A movie theater charges $11.00 for adults, $6.50 for children, and $9.00 for senior citizens. One day the theater sold 405 tickets and collected $3315 in receipts.Twice as many children’s tickets were sold as adult tickets. How many adults, children, and senior citizens went to the theater that day? 81. Nutrition A dietitian wishes a patient to have a meal that has ( ) 66 grams g of protein, 94.5 g of carbohydrates, and ( ) 910 milligrams mg of calcium. The hospital food service tells the dietitian that the dinner for today is chicken, corn, and 2% milk. Each serving of chicken has 30 g of protein,
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