985 CHAPTER 9 Review Exercises Solve each problem using the Gauss-Jordan method. 31. Mixing Teas Three kinds of tea worth $4.60, $5.75, and $6.50 per lb are to be mixed to get 20 lb of tea worth $5.25 per lb. The amount of $4.60 tea used is to be equal to the total amount of the other two kinds together. How many pounds of each tea should be used? 32. Mixing Solutions A 5% solution of a drug is to be mixed with some 15% solution and some 10% solution to make 20 ml of 8% solution. The amount of 5% solution used must be 2 ml more than the sum of the other two solutions. How many milliliters of each solution should be used? 33. (Modeling) Master’s Degrees During the period 1977–2017, the numbers of master’s degrees awarded to both males and females grew. If x = 0 represents 1977 and x = 40 represents 2017, the number of master’s degrees earned (in thousands) are closely modeled by the following system. y = 3.860x + 171.5 Males y = 8.200x + 149.8 Females Solve the system to find the year in which males and females earned the same number of master’s degrees. What was the equivalent number, to the nearest thousand, of master’s degrees earned in that year? (Data from National Center for Education Statistics.) 34. (Modeling) Comparing Prices One refrigerator sells for $700 and uses $85 worth of electricity per year. A second refrigerator is $100 more expensive but costs only $25 per year to run. Assuming that there are no repair costs, the costs to run the refrigerators over a 10-yr period are given by the following system of equations. Here, y represents the total cost in dollars, and x is time in years. y = 700 + 85x y = 800 + 25x In how many years will the costs for the two refrigerators be equal? What are the equivalent costs at that time? Evaluate each determinant. 35. 2 -1 2 8 92 36. 2 -2 0 4 32 37. 2 x 2x 4x 8x2 38. 3 -2 3 -1 4 0 0 1 2 33 39. 3 -1 4 5 2 0 -1 3 3 23 40. 3 -3 6 7 2 -4 1 7 -14 43 Use Cramer’s rule to solve each system of equations. If D= 0, use another method to determine the solution set. 41. 3x + 7y = 2 5x - y = -22 42. 3x + y = -1 5x + 4y = 10 43. 6x + y = -3 12x + 2y = 1 44. 3x + 2y + z = 2 4x - y + 3z = -16 x + 3y - z = 12 45. x + y = -1 2y + z = 5 3x - 2z = -28 46. 5x - 2y - z = 8 -5x + 2y + z = -8 x - 4y - 2z = 0
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