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Material Type: Quiz; Class: COLLEGE ALGEBRA; Subject: MATHEMATICS; University: La Sierra University; Term: Fall 2004;
Typology: Quizzes
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Math 121, Quiz 5, November 5, 2004
Name: Answers and Hints
Answer. Let x be the amount invested in stocks and let y be the amount invested in bonds. Then x + y = 3000 and. 045 x +. 08 y = 177. Using the substitution method, we put y = 3000 โ x into the second equation to get. 045 x + .08(3000 โ x) = 177, which simplifies to โ. 035 x + 240 = 177, and so. 035 x = 63, or x = 63 /.035 = 1800. Therefore, y = 1200. So, $1800 was invested in stocks, and $1200 was invested in bonds. Check: 4.5% of 1800 + 8% of 1200 is 81 + 96 = 177.
Answer. There are several possible methods to solve this. Using substitution, the second equation implies x = 5y โ 8, and we substitute 5y โ 8 for x in the first equation to get 3(5y โ 8) + 4y = โ5, or 19y โ 24 = โ5, and so y = 1 and x = 5 โ 8 = โ3. Check: 3(โ3) + 4(1) = โ9 + 4 = โ5 and โ 3 โ 5(1) = โ 3 โ 5 = โ8, thus both equations are satisfied by x = โ3 and y = 1.
(a) For which value(s) of c, if any, does the system have infinitely many solutions? (b) For which value(s) of c, if any, does the system have a unique solution? (c) For which value(s) of c, if any, does the system have no solution? (d) Find the solution to the system if c = 1.
Answer. (a) No values of c lead to infinitely many solutions. All values of c are accounted for in the cases for (b) and (c) below. (b) c 6 = 0 (c) c = 0, because then 0 = 2 which is impossible. (d) If c = 1, then z = 2, and so y โ 6 = โ5, or y = 1, and then x โ 2 + 2 = 5, or x = 5. Thus the solution is x = 5, y = 1 and z = 2.