# 64Systems of Linear Equations; Matrices1.95 grams of phosphorus per pound, while molassesvides 3.35 grams of calcium per pound and 0.36 gChapter 22.2 Sys53. Cost of Food in Japan In Kyotoshi, Japan, the cost of threebowls of noodles and two cartons of fresh milk is 2153 yen.Three cartons of fresh milk cost 89 yen more than one bowlof noodles. What is the cost of a bowl of noodles? A cartonphosphorus per pound. How many pounds each of roleoats and molasses should the farmer feed the yearlingorder to meet the daily requirements?OBJECTIVESSource: Balancing Rations for Horses, R. D. Setzler,of fresh milk?Source: Statistics Bureau and Statistics Center, Ministry ofPublic Management, Home Affairs, Posts and Telecommuni-cations, Japan, 2002.Washington State University.60. Restaurant Management A restaurant manager wants topurchase 200 sets of dishes. One design costs \$25 perwhile another costs \$45 per set. If she only has \$7400 to54. Cost of Fast Food Four large cheeseburgers and two choco-late shakes cost a total of \$7.90. Two shakes cost 15¢ morespend, how many of each design should be ordered?than one cheeseburger. What is the cost of a cheeseburger? Ashake?55. Computing a Refund The grocery store we use does notmark prices on its goods. My wife went to this store, boughtthree 1-pound packages of bacon and two cartons of eggs,and paid a total of \$7.45. Not knowing that she went to thestore, I also went to the same store, purchased two 1-poundpackages of bacon and three cartons of eggs, and paid atotal of \$6.45. Now we want to return two 1-pound pack-ages of bacon and two cartons of eggs. How much will berefunded?61. Theater Revenues A Broadway theater has 500 seats, divid.ed into orchestra, main, and balcony seating. Orchestra seatsell for \$50, main seats for \$35, and balcony seats for \$25.1all the seats are sold, the gross revenue to the theater is\$17,100. If all the main and balcony seats are sold, but onlyhalf 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 foradults, \$4.50 for children, and \$6.00 for senior citizens. Oneday the theater sold 405 tickets and collected \$2320 inreceipts. There were twice as many children's tickets sold asadult tickets. How many adults, children, and senior citizenswent to the theater that day?56. Blending Coffees A coffee manufacturer wants to market anew blend of coffee that will cost \$5 per pound by mixing\$3.75-per-pound coffee and \$8-per-pound coffee. Whatamounts of the \$3.75-per-pound coffee and \$8-per-poundcoffee should be blended to obtain the desired mixture?63. Investments Kelly has \$20,000 to invest. As her financialplanner, you recommend that she diversify into three invest-ments: Treasury Bills that yield 5% simple interest, TreasulBonds that yield 7% simple interest, and corporate bonthat yield 10% simple interest. Kelly wishes to earn \$1390per year in income. Also, Kelly wants her investment in[Hint: Assume the total weight of the desired blend is 100pounds.]57. Pharmacy A doctor's prescription calls for a daily intake ofliquid containing 40 mg of vitamin C and 30 mg of vitaminD. Your pharmacy stocks two liquids that can be used: onecontains 20% vitamin C and 30% vitamin D, the other 40%vitamin C and 20% vitamin D. How many milligrams ofeach liquid should be mixed to fill the prescription?Treasury Bills to be \$3000 more than her investment in colporate bonds. How much money should Kelly place in eachinvestment?64. Make up a system of two linear equations containing twOvariables that has:58. Pharmacy A doctor's prescription calls for the creation ofpills that contain 12 units of vitamin B12 and 12 units of vit-amin E. Your pharmacy stocks two powders that can be usedto 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 solutionsथdGive the three systems to a friend to solve and critique.59. Diet Preparation A 600- to 700-pound yearling horse needs33.0 grams of calcium and 21.0 grams of phosphorus perday for a healthy diet. A farmer provides a combination ofrolled oats and molasses to provide those nutrients. Rolledoats provide 0.41 grams of calcium per pound and65. Write a brief paragraph outlining your strategy for solvingsystem of two linear equations containing two variables.66. Do you prefer the method of substitution or the method ofelimination for solving a system of two linear equations con-taining two variables? Give reasons.

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Need. Help with number 63

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Step 1

Let us say he invests \$x in Treasury Bills, \$y in Treasury Bond, \$z in Corporate Bond

The total invest

--- Eq 1

The interest rates:

---- Eq 2

Also, given

--- Eq 3

Step 2

Now, substituting Eq 3 in Eq1 and Eq 2 we get

Step 3

Solving,

...

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