292 Chapter 3 Systems of Linear Equations and Inequalities 32. Annie and Maria traveled overseas for 7 days and stayed in three different hotels in three different cities: Stockholm, Sweden; Oslo, Norway; and Paris, France. The total bill for all seven nights (not including tax) was $1040.The total tax was $106.The nightly cost (excluding tax) to stay at the hotel in Paris was $80 more than the nightly cost (excluding tax) to stay in Oslo. Find the cost per night for each hotel excluding tax. Number Cost/Night Tax City of Nights ($) Rate Paris, 1 x 8% France Stockholm, 4 y 11% Sweden Oslo, 2 z 10% Norway 33. Walter had $25,000 to invest. He split the money into three types of investment: small caps earning 6%, global market investments earning 10%, and a balanced fund earning 9%. He put twice as much money in the global account as he did in the balanced fund. If his earnings for the first year totaled $2160, how much did he invest in each account? 34. Raeann deposited $8000 into three accounts at her credit union: a checking account that pays 1.2% interest, a savings account that pays 2.5% interest, and a money market account that pays 3% interest. If she put 3 times more money in the 3% account than she did in the 1.2% account, and her total interest for 1 yr was $202, how much did she deposit into each account? Concept 4: Solving Inconsistent Systems and Systems of Dependent Equations For Exercises 35–46, solve the system. If the system does not have a unique solution, state whether the system is inconsistent or the equations are dependent. (See Examples 1, 4, and 5.) 35. 36. 37. 38. 39. 40. 3 10 41. 42. 43. 44. 45. 46. Expanding Your Skills The systems in Exercises 47–50 are called homogeneous systems because each system has (0, 0, 0) as a solution. However, if the equations are dependent, the system will have infinitely many more solutions. For each system determine whether (0, 0, 0) is the only solution or if the equations are dependent. 47. 48. 49. 50. 5x y 0 4y z 0 5x 5y z 0 4x 2y 3z 0 8x y z 0 2x y 3 2 z 0 2x 4y z 0 x 3y z 0 3x y 2z 0 2x 4y 8z 0 x 3y z 0 x 2y 5z 0 0.4x 0.3y 0 0.3y 0.1z 0.1 0.4x 0.1z 1.2 0.1y 0.2z 0.2 0.1x 0.1y 0.1z 0.2 0.1x 0.3z 0.2 2x y 3 2y 16z 10 7x 3y 4z 8 2x y 31z 12 3x 21y 2z2 1 212x 3z2 6 2y 2x 3y 3z 15 3x 6y 6z 23 9x 3y 6z 8 3x y z 8 4x 2y 3z 3 2x 3y 2z 1 12 x 14 y z 3 18 x 14 y 14 z 98 x y 23 z 13 1 2x 23 y 52 1 5x 12 z 13 y 14 z 34 3x 2y z 3 x 3y z 4 6x 4y 2z 1 6x 2y 2z 2 4x 8y 2z 5 2x 4y z 2 x y z 2x 4y 2z 6 3x 6y 3z 9 2x y 3z 2 x y 2z 4 2x 2y 4z 8
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