64 Systems of Linear Equations; Matrices 1.95 grams of phosphorus per pound, while molasses vides 3.35 grams of calcium per pound and 0.36 g Chapter 2 2.2 Sys 53. Cost of Food in Japan In Kyotoshi, Japan, the cost of three bowls of noodles and two cartons of fresh milk is 2153 yen. Three cartons of fresh milk cost 89 yen more than one bowl of noodles. What is the cost of a bowl of noodles? A carton phosphorus per pound. How many pounds each of role oats and molasses should the farmer feed the yearling order to meet the daily requirements? OBJECTIVES Source: Balancing Rations for Horses, R. D. Setzler, of fresh milk? Source: Statistics Bureau and Statistics Center, Ministry of Public Management, Home Affairs, Posts and Telecommuni- cations, Japan, 2002. Washington State University. 60. Restaurant Management A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per while another costs $45 per set. If she only has $7400 to 54. Cost of Fast Food Four large cheeseburgers and two choco- late shakes cost a total of $7.90. Two shakes cost 15¢ more spend, how many of each design should be ordered? than one cheeseburger. What is the cost of a cheeseburger? A shake? 55. Computing a Refund The grocery store we use does not mark prices on its goods. My wife went to this store, bought three 1-pound packages of bacon and two cartons of eggs, and paid a total of $7.45. Not knowing that she went to the store, I also went to the same store, purchased two 1-pound packages of bacon and three cartons of eggs, and paid a total of $6.45. Now we want to return two 1-pound pack- ages of bacon and two cartons of eggs. How much will be refunded? 61. Theater Revenues A Broadway theater has 500 seats, divid. ed into orchestra, main, and balcony seating. Orchestra seat sell for $50, main seats for $35, and balcony seats for $25.1 all the seats are sold, the gross revenue to the theater is $17,100. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $14,600. How many are there of each kind of seat? 62. Theater Revenues A movie theater charges $8.00 for adults, $4.50 for children, and $6.00 for senior citizens. One day the theater sold 405 tickets and collected $2320 in receipts. There were twice as many children's tickets sold as adult tickets. How many adults, children, and senior citizens went to the theater that day? 56. Blending Coffees A coffee manufacturer wants to market a new blend of coffee that will cost $5 per pound by mixing $3.75-per-pound coffee and $8-per-pound coffee. What amounts of the $3.75-per-pound coffee and $8-per-pound coffee should be blended to obtain the desired mixture? 63. Investments Kelly has $20,000 to invest. As her financial planner, you recommend that she diversify into three invest- ments: Treasury Bills that yield 5% simple interest, Treasul Bonds that yield 7% simple interest, and corporate bon that yield 10% simple interest. Kelly wishes to earn $1390 per year in income. Also, Kelly wants her investment in [Hint: Assume the total weight of the desired blend is 100 pounds.] 57. Pharmacy A doctor's prescription calls for a daily intake of liquid containing 40 mg of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used: one contains 20% vitamin C and 30% vitamin D, the other 40% vitamin C and 20% vitamin D. How many milligrams of each liquid should be mixed to fill the prescription? Treasury Bills to be $3000 more than her investment in col porate bonds. How much money should Kelly place in each investment? 64. Make up a system of two linear equations containing twO variables that has: 58. Pharmacy A doctor's prescription calls for the creation of pills that contain 12 units of vitamin B12 and 12 units of vit- amin E. Your pharmacy stocks two powders that can be used to make these pills: one contains 20% vitamin B12 and 30% vitamin E, the other 40% vitamin B12 and 20% vitamin E. How many units of each powder should be mixed in each (a) No solution (b) Exactly one solution (c) Infinitely many solutions थd Give the three systems to a friend to solve and critique. 59. Diet Preparation A 600- to 700-pound yearling horse needs 33.0 grams of calcium and 21.0 grams of phosphorus per day for a healthy diet. A farmer provides a combination of rolled oats and molasses to provide those nutrients. Rolled oats provide 0.41 grams of calcium per pound and 65. Write a brief paragraph outlining your strategy for solving system of two linear equations containing two variables. 66. Do you prefer the method of substitution or the method of elimination for solving a system of two linear equations con- taining two variables? Give reasons.