Michael Hoy - Student Solutions Manual for Mathematics for Economics, fourth edition

2022 Massachusetts Institute of Technology

All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.

ISBN 978-0-262-54372-9

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Note: For answers to chapter 17, see the back of the text. No further solutions are required.

This Student Solutions Manual contains the full solutions to the odd-numbered questions in the text. Brief answers to these questions were also given at the end of the text.

Chapter 1 is a review of basic arithmetic and algebra, which may prove to be useful to those students who need to have a quick refresher course in basic math. Each section contains self-tests to help you identify gaps in your knowledge. The remaining chapters follow the chapter sequence in the text, and are organized in corresponding sections. Only odd-numbered solutions are provided. Chapter 17 has a number of exercises for which the answers in the text are sufficient. We have therefore omitted this chapter from the manual.

The figures are numbered according to chapter, section, and question number, so it is easy to associate a figure with its corresponding question. For example, figure 13.3.1 is the figure for question 1 of section 3 in chapter 13. Figure 12.R.5 is the figure for question 5 of the chapter review in chapter 12.

Updated information about the text and the solutions manual is available on our World Wide Web site at http://mitpress.mit.edu/math_econ4. Some answers here are for questions based on worked examples that have been moved from the text to the website. In those cases we have put "Website example" at the beginning of the answer.

Michael Hoy
John Livernois
Chris McKenna
Ray Rees
Thanasis Stengos

In this chapter we present a review of basic arithmetic and algebra along with a series of tests designed to help you identify your initial strengths and weaknesses. You should read this chapter during the first few days of your course. It is possible that the instructor will not be covering this basic material in class.

The chapter is in two sections. Section 1.1 reviews basic arithmetic and section 1.2 reviews basic algebra. Each section is in turn composed of three parts: a pretest, a review, and an exit test. Use the pretest to identify your strengths. If you have difficulties, you should read the review part carefully. If you have no difficulties, you could just refresh your memory by reading the review quickly. The exit test helps you assess what you have learned from studying the review. If you remain unsure, you should discuss your problems with the instructor. Answers to all self-tests are on page 26.

1. What is 1/10 of 3/4?
   1. a) 1/10
   2. a) 15/5
   3. b) 2/15
   4. b) 3/40
   5. c) None of the above
2. One number is 3 more than 2 times another. Their sum is 21. Find the numbers.
   1. a) 7, 14
   2. a) 2, 19
   3. b) 6, 15
   4. c) 10, 11
   5. d) 8, 13
3. Evaluate .
   1. a)
   2. b)
   3. c)
   4. d)
   5. e) None of the above
4. What is the product of ?
   1. a)
   2. b) 12
   3. c)
   4. d)
   5. e) 9
5. What is the value of the expression 1/[1+1/(1+1/4)]?
   1. a) 9=5
   2. b) 5=9
   3. c) 1=2
   4. d) 3
   5. e) 5
6. Which of the following has the smallest value?
   1. a) 1/0.2
   2. b) 0.1/2
   3. c) 0.1/1
   4. d) 0.2/0.1
   5. e) 2/0.2
7. Which is the smallest number?
   1. a) 5(105)/3(105)
   2. b) 0.3/0.2
   3. c) 0.3/0.3(104)
   4. d) 5(103)/0.1
   5. e) 0.3/0.3(102)
8. Evaluate 103 + 105.
   1. a) 108
   2. b) 1015
   3. c) 208
   4. d) 210
   5. e) 101,000
9. Evaluate 10 {(23 + 27)/[3 2(8 10)]}.
   1. a) 5
   2. b) 15
   3. c) 25
   4. d) 10
   5. e) 35
10. Which is the largest fraction?
    1. a) 1/5
    2. b) 2/9
    3. c) 2/11
    4. d) 4/16
    5. e) 3/19
11. Evaluate .
    1. a) 4
    2. b) 4
    3. c) 16
    4. d) 1/8
    5. e) 1/4
12. Evaluate (2100 + 298)/(2100 298).
    1. a) 2198
    2. b) 299
    3. c) 64
    4. d) 8
    5. e) 5/3
13. Evaluate (24 + 21)/23.
    1. a) 9/27
    2. b) 18
    3. c) 1/2
    4. d) 23
    5. e) 9/2
14. What is 1/10 of 3/8?
    1. a) 1/8
    2. b) 15/4
    3. c) 15/2
    4. d) 4/15
    5. e) None of the above
15. Evaluate 3/6 + 2/12.
    1. a) 1/12
    2. b) 5/6
    3. c) 2/3
    4. d) 8/9
    5. e) 5/18
16. Simplify .
    1. a)
    2. b)
    3. c)
    4. d)
    5. e) 50
17. Evaluate .
    1. a)
    2. b)
    3. c) 0
    4. d) 3
    5. e)
18. The cheapest among the following prices is