903 9.2 Matrix Solution of Linear Systems Solve each problem using the Gauss-Jordan method. 69. Daily Wages Dan is a building contractor. If he hires 7 day laborers and 2 concrete finishers, his payroll for the day is $1384. If he hires 1 day laborer and 5 concrete finishers, his daily cost is $952. Find the daily wage for each type of worker. 70. Mixing Nuts At the Everglades Nut Company, 5 lb of peanuts and 6 lb of cashews cost $33.60, while 3 lb of peanuts and 7 lb of cashews cost $32.40. Find the cost of a single pound of peanuts and a single pound of cashews. 71. Unknown Numbers Find three numbers whose sum is 20, if the first number is three times the difference between the second and the third, and the second number is two more than twice the third. 72. Car Sales Quota To meet a sales quota, a car salesperson must sell 24 new cars, consisting of small, medium, and large cars. She must sell 3 more small cars than medium cars, and the same number of medium cars as large cars. How many of each size must she sell? 73. Mixing Acid Solutions A chemist has two prepared acid solutions, one of which is 2% acid by volume, the other 7% acid. How many cubic centimeters of each should the chemist mix together to obtain 40 cm3 of a 3.2% acid solution? Strength cm3 of Solution cm3 of Pure Acid 2% 7% 3.2% 40 74. Borrowing Money A small company took out three loans totaling $25,000. The company was able to borrow some of the money at 4% interest. It borrowed $2000 more than one-half the amount of the 4% loan at 6%, and the rest at 5%. The total annual interest was $1220. How much did the company borrow at each rate? Loan Amount Rate (as a decimal) Annual Interest 0.04 0.06 0.05 75. Investing Money An investor deposited some money at 1.5% annual interest, and two equal but larger amounts at 2.2% and 2.4%. The total amount invested was $25,000, and the total annual interest earned was $535. How much was invested at each rate? 76. Investing Money An investor deposited some money at 1.75% annual interest, some at 2.25%, and twice as much as the sum of the first two at 2.5%. The total amount invested was $30,000, and the total annual interest earned was $710. How much was invested at each rate? 77. Planning a Diet In a special diet for a hospital patient, the total amount per meal of food groups A, B, and C must equal 400 g. The diet should include one-third as much of group A as of group B. The sum of the amounts of group A and group C should equal twice the amount of group B. How many grams of each food group should be included? (Give answers to the nearest tenth.)
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