MATH 163 A. ASSIGNMENT #3 Using an augmented matrix , solve the following systems of equations. 2z 4 y z 2 x y 2z 5 ________________________________________________________________________ x B. With the use of calculator technology, solve each system of equations, and interpret your results. 1. 2x 2 y z 9 x z4 4 y 3 z 17 2. 2x 3y z 6 x 2 y 4 z 4 x 5 y 3 z 10 3. x 2y 4 x 2y 0 4 x 3 y 12 4. x 2 y 4z 2 x y 2z 1 y 2z 7 x 2 y 6 z 18 5. 6. x y 2z 5 2 x 5 y 15 z 46 _______________________________________________________________________ x y z w 1 3 x 2 y 4 z 2w 1 4 x y 5z w 5 C. Set up an appropriate system of equations for each question, and solve. 1. A child has $14.35 worth of nickels and dimes in her piggy bank. There is a total of 165 coins. How many of each does she have? 2. The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labour) is $42 and $30 per acre, respectively. Mr. Johnson has $18,600 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? 3. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a new fleet of automobiles consisting of compact, intermediate and full-size cars. Compacts cost $12,000 each, intermediate-size cars cost $18,000 each, and fullsize cars cost $24,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume the entire budget will be used. 4. At the beginning of a new semester, Andy makes plans for a successful semester. He allocates 42 hours per week for study time for the four courses he is taking: Math, English, Chemistry and History. He decides to allocate half of his time to Math and English, and twice as much time to Math as to English. He decides to allocate twice as much to English as to History. (a) Find a system of equations that represents this information. (b) Solve the system to determine the number of hours allocated to each subject