Solutions Manual for Finite Mathematics by Carla C. Morris & Robert M. Stark – Step-by-Step Exercise Solutions

SOLUTIONS MANUAL

,CONTENTS



1 LINEAR EQUATIONS AND
MATHEMATICAL CONCEPTS 1

2 MATHEMATICS OF FINANCE 20

3 MATRIX ALGEBRA 29

4 LINEAR PROGRAMMING – GRAPHICAL SOLUTIONS
47

5 LINEAR PROGRAMMING – SIMPLEX METHOD 65

6 LINEAR PROGRAMMING – APPLICATION MODELS92

7 SET AND PROBABILITY RELATIONSHIPS 96

8 RANDOM VARIABLES AND
PROBABILITY DISTRIBUTIONS 117


9 MARKOV CHAINS 129

10 MATHEMATICAL STATISTICS 140

11 ENRICHMENT IN FINITE MATHEMATICS 149

,CHAPTER 1




LINEAR EQUATIONS AND
MATHEMATICAL CONCEPTS


EXERCISES 1.1

1. 3x + 1 = 4x − 5
1= x−5
x=6 conditional equation

3. 5(x + 1) + 2(x − 1) = 7x + 6
5x + 5 + 2x − 2 = 7x + 6
7x + 3 = 7x + 6 contradiction

5. 4(x + 3) = 2(2x + 5)
4x + 12 = 4x + 10 contradiction




1

, 2 LINEAR EQUATIONS AND MATHEMATICAL CONCEPTS


7. 5x − 3 = 17
5x = 20
x=4

9. 2x = 4x − 10
2x − 4x = −10
−2x = −10
x=5

11. 4x − 5 = 6x − 7
−5 + 7 = 6x −
4x 2 = 2x
1=x

13. 0.6x = 30
x = 30∕ 0.60 = 50

15. 2∕ 3 = (4∕ 5) x − (1∕ 3) multiply by 15 to eliminate fractions
1 (2∕ 3) = 15 {(4∕ 5) x − (1∕ 3)}
10 = 12x − 5
15 = 12x
5∕ 4 = x

17. 5(x − 4) = 2x + 3(x − 7)
5x − 20 = 2x + 3x − 21
5x − 20 = 5x − 21
No solution

19. 3s − 4 = 2s + 6
s−4= 6
s = 10