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Solution Manual for A Survey of Mathematics with Applications, 11th Edition

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    S OLUTIONS M ANUAL J AMES L APP A S URVEY OF M ATHEMATICS WITH A PPLICATIONS E LEVENTH E DITION Allen R. Angel Monroe Community College Christine D. Abbott Monroe Community College Dennis C. Runde State College of Florida

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    Table of Contents Chapter 1: Critical Thinking Skills 1.1: Inductive and Deductive Reasoning ..................................................................................................1 1.2: Estimation Techniques ......................................................................................................................3 1.3: Problem-Solving Procedures .............................................................................................................5 Review Exercises ............................................................................................................................11 Chapter Test ....................................................................................................................................14 Chapter 2: Sets 2.1: Set Concepts ....................................................................................................................................17 2.2: Subsets.............................................................................................................................................19 2.3: Venn Diagrams and Set Operations ................................................................................................21 2.4: Venn Diagrams with Three Sets and Verification of Equality of Sets ............................................26 2.5: Applications of Sets ........................................................................................................................32 2.6: Infinite Sets .....................................................................................................................................35 Review Exercises ............................................................................................................................37 Chapter Test ....................................................................................................................................40 Chapter 3: Logic 3.1: Statements and Logical Connectives ...............................................................................................43 3.2: Truth Tables for Negation, Conjunction, and Disjunction ..............................................................45 3.3: Truth Tables for the Conditional and Biconditional ........................................................................54 3.4: Equivalent Statements .....................................................................................................................65 3.5: Symbolic Arguments .......................................................................................................................73 3.6: Euler Diagrams and Syllogistic Arguments ....................................................................................80 3.7: Switching Circuits ...........................................................................................................................83 Review Exercises ............................................................................................................................87 Chapter Test ....................................................................................................................................93 Chapter 4: Systems of Numeration 4.1: Additive, Multiplicative, and Ciphered Systems of Numeration.....................................................97 4.2: Place-Value or Positional-Value Numeration Systems ...................................................................99 4.3: Other Bases ...................................................................................................................................101 4.4: Perform Computations in Other Bases ..........................................................................................106 4.5: Early Computational Methods.......................................................................................................111 Review Exercises ..........................................................................................................................115 Chapter Test ..................................................................................................................................119 Chapter 5: Number Theory and the Real Number System 5.1: Number Theory .............................................................................................................................121 5.2: The Integers ...................................................................................................................................125 5.3: The Rational Numbers...................................................................................................................128 5.4: The Irrational Numbers .................................................................................................................133 5.5: Real Numbers and Their Properties ..............................................................................................136 5.6: Rules of Exponents and Scientific Notation ..................................................................................138 5.7: Arithmetic and Geometric Sequences ...........................................................................................141 5.8: Fibonacci Sequence .......................................................................................................................146 Review Exercises ..........................................................................................................................148 Chapter Test ..................................................................................................................................152

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    Chapter 6: Algebra, Graphs, and Functions 6.1: Order of Operations and Solving Equations ..................................................................................153 6.2: Formulas ........................................................................................................................................157 6.3: Applications of Algebra ................................................................................................................162 6.4: Variation ........................................................................................................................................167 6.5: Solving Linear Inequalities ...........................................................................................................171 6.6: Graphing Linear Equations ...........................................................................................................176 6.7: Solving Systems of Linear Equations............................................................................................184 6.8: Linear Inequalities in Two Variables and Systems of Linear Inequalities ....................................195 6.9: Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula ..............204 6.10: Functions and Their Graphs ..........................................................................................................210 Review Exercises ..........................................................................................................................217 Chapter Test ..................................................................................................................................227 Chapter 7: The Metric System 7.1: Basic Terms and Conversions Within the Metric System .............................................................231 7.2: Length, Area, and Volume ............................................................................................................232 7.3: Mass and Temperature ..................................................................................................................235 7.4: Dimensional Analysis and Conversions to and from the Metric System ......................................237 Review Exercises ..........................................................................................................................241 Chapter Test ..................................................................................................................................243 Chapter 8: Geometry 8.1: Points, Lines, Planes, and Angles..................................................................................................245 8.2: Polygons ........................................................................................................................................248 8.3: Perimeter and Area ........................................................................................................................252 8.4: Volume and Surface Area .............................................................................................................256 8.5: Transformational Geometry, Symmetry, and Tessellations ..........................................................260 8.6: Topology .......................................................................................................................................265 8.7: Non-Euclidean Geometry and Fractal Geometry ..........................................................................266 Review Exercises ..........................................................................................................................267 Chapter Test ..................................................................................................................................270 Chapter 9: Mathematical Systems 9.1: Groups ...........................................................................................................................................273 9.2: Finite Mathematical Systems ........................................................................................................274 9.3: Modular Arithmetic .......................................................................................................................277 9.4: Matrices .........................................................................................................................................282 Review Exercises ..........................................................................................................................288 Chapter Test ..................................................................................................................................290 Chapter 10: Consumer Mathematics 10.1: Percent ...........................................................................................................................................293 10.2: Personal Loans and Simple Interest ..............................................................................................295 10.3: Compound Interest ........................................................................................................................300 10.4: Installment Buying ........................................................................................................................304 10.5: Buying a House with a Mortgage ..................................................................................................310 10.6: Ordinary Annuities, Sinking Funds, and Retirement Investments ................................................317 Review Exercises ..........................................................................................................................318 Chapter Test ..................................................................................................................................322

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    Chapter 11: Probability 11.1: Empirical and Theoretical Probabilities ........................................................................................325 11.2: Odds ..............................................................................................................................................328 11.3: Expected Value (Expectation) .......................................................................................................332 11.4: Tree Diagrams ...............................................................................................................................336 11.5: OR and AND Problems ..................................................................................................................340 11.6: Conditional Probability .................................................................................................................344 11.7: The Fundamental Counting Principle and Permutations ...............................................................347 11.8: Combinations ................................................................................................................................349 11.9: Solving Probability Problems by Using Combinations .................................................................351 11.10: Binomial Probability Formula .......................................................................................................353 Review Exercises ..........................................................................................................................355 Chapter Test ..................................................................................................................................359 Chapter 12: Statistics 12.1: Sampling Techniques and Misuses of Statistics ............................................................................361 12.2: Frequency Distributions and Statistical Graphs ............................................................................363 12.3: Measures of Central Tendency and Position .................................................................................368 12.4: Measures of Dispersion .................................................................................................................374 12.5: The Normal Curve .........................................................................................................................379 12.6: Linear Correlation and Regression ................................................................................................385 Review Exercises ..........................................................................................................................395 Chapter Test ..................................................................................................................................400 Chapter 13: Graph Theory 13.1: Graphs, Paths, and Circuits ...........................................................................................................403 13.2: Euler Paths and Euler Circuits.......................................................................................................404 13.3: Hamilton Paths and Hamilton Circuits ..........................................................................................408 13.4: Trees ..............................................................................................................................................411 Review Exercises ..........................................................................................................................415 Chapter Test ..................................................................................................................................417 Chapter 14: Voting and Apportionment 14.1: Voting Methods .............................................................................................................................419 14.2: Flaws of the Voting Methods ........................................................................................................423 14.3: Apportionment Methods................................................................................................................428 14.4: Flaws of the Apportionment Methods ...........................................................................................433 Review Exercises ..........................................................................................................................438 Chapter Test ..................................................................................................................................445

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    Section 1.1: Inductive and Deductive Reasoning 1 Chapter One: Critical Thinking Skills Section 1.1: Inductive and Deductive Reasoning 1. Natural 2. Divisible 3. Counterexample 4. Hypothesis 5. Inductive 6. Deductive 7. Deductive 8. Inductive 9. 5 3 15   10. 19 10 190   11. (1 4) (4 6) (4 6) (1 4) 1 1 5 10 10 5     12. 5 100, 000 10  13. 14. 15. 16. 17. 9, 11, 13 (Add 2 to previous number.) 18. 16, 19, 22 (Add 3 to the previous number.) 19. 5, –5, 5 (Alternate 5 and –5.) 20. 16, –32, 64 (Multiply previous number by –2.) 21. 1 1 1 , , 5 6 7 (Increase denominator value by 1.) 22. 1 1 1 , , 9 11 13 (Increase denominator value by 2.) 23. 21, 28, 36 (15 6 21, 21 7 28, 28 8 36)       24. 16, 22, 29 (Add 1, then 2, then 3, ….) 25. 34, 55, 89 (Each number in the sequence is the sum of the previous two numbers.) 26. 76, 123, 199 (Each number in the sequence is the sum of the previous two numbers.) 27. There are three letters in the pattern. 39 3 117,   so, the 117th entry is the second R in the pattern. Therefore, the 118th entry is Y. 28. a) Answers will vary. b) The sum of the digits is 9. c) The sum of the digits in the product when a one- or two-digit number is multiplied by 9 is divisible by 9. 29. a) 36, 49, 64 b) Square the numbers 6, 7, 8, 9 and 10. c) 8 8 64, 9 9 81;     72 is not a square number since it falls between the two square numbers 64 and 81. 30. a) 28 and 36 b) To find the 7th triangular number, add 7 to the 6th triangular number. To find the 8th triangular number, add 8 to the 7th triangular number. To find the 9th triangular number, add 9 to the 8th triangular number. To find the 10th triangular number, add 10 to the 9th triangular number. To find the 11th triangular number, add 11 to the 10th triangular number. c) 36 9 45,   45 10 55,   55 11 66;   66 12 78;   72 is not a triangular number since it falls between the consecutive triangular numbers 66 and 78. 31. Blue: 1, 5, 7, 10, 12; Purple: 2, 4, 6, 9, 11; Yellow: 3, 8 32. a) 19 (Each new row has two additional triangles.) b) 1 3 5 7 9 11 13 15 17 19 100           33. a) $3700 b) We are using observation of specific cases to make a prediction.

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    2 Chapter 1: Critical Thinking Skills 34. a) $410 b) We are using observation of specific cases to make a prediction. 35. 36. 37. a) You should obtain the original number. b) You should obtain the original number. c) Conjecture: The result is always the original number. d) 3 6 3 6 3 3 6 2 2 2 3 3 3 n n n n n n n n +   +  = + = +  + - = 38. a) You should obtain twice the original number. b) You should obtain twice the original number. c) Conjecture: The result is always twice the original number. d) 4 6 4 6 4 4 6 2 3 2 3 3 2 2 2 2 n n n n n n n n              39. a) You should obtain the number 5. b) You should obtain the number 5. c) Conjecture: The result is always the number 5. d) 2 10 2 10 1 ( 1) 2 1 2 1 9 2 10 5 5 5 2 2 2 n n n n n n n n n n n n                       40. a) You should obtain the number 0. b) You should obtain the number 0. c) Conjecture: The result is always the number 0. d) 10 10 10 5 10 10 10 0 5 5 n n n n n n n n n                      41. 3 5 15 is one counterexample.   42. 10 11 12 = 33, which is not a three digit number.   43. Two is a counting number. The sum of 2 and 3 is 5. Five divided by two is 5 2, which is not an even number. 44. 900 is a three-digit number. The product of 900 and 900 is 810,000, which is not a five-digit number. 45. One and two are counting numbers. The difference of 1 and 2 is 1 2 1    , which is not a counting number. 46. The sum of the odd numbers 1 and 5 is 6, which is not divisible by 4. 47. a) The sum of the measures of the interior angles should be 180 .  b) Yes, the sum of the measures of the interior angles should be 180 .  c) Conjecture: The sum of the measures of the interior angles of a triangle is 180 .  48. a) The sum of the measures of the interior angles should be 360 .  b) Yes, the sum of the measures of the interior angles should be 360 .  c) Conjecture: The sum of the measures of the interior angles of a quadrilateral is 360 .  49. Inductive reasoning: a general conclusion is obtained from observation of specific cases.

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    Section 1.2: Estimation Techniques 3 50. Inductive reasoning: a general conclusion is obtained from observation of specific cases. 51. 129; The numbers in the positions of each inner 4 4  square are determined as follows. a b c a b c   52. 1881, 8008, 8118 (They look the same when looked at in a mirror.) 53. c Section 1.2: Estimation Techniques Answers in this section will vary depending on how you round your numbers. The answers may differ from the answers in the back of the textbook. However, your answers should be something near the answers given. All answers are approximate.) 1. Estimation 2. Equal 3. 26.9 67.3 219 143.3 30 67 220 143 460         4. 86 47.2 289.8 532.4 12.8 90 50 290 530 10 970           5. 197,500 4.063 200, 000 4.000 50, 000     6. 405 400 8000 0.049 0.05   7. 1776 0.0098 1800 0.01 18     8. 0.63 1523 0.6 1500 900     9. 23.97 7.05 24 7 17     10. 400.15 297.87 400 300 100     11. 22% 9116 20% 9000 0.20 9000 1800       12. 11% of 8221 10% of 8000 0.10 8000 800     13. $91.35 $90 $30 3 3   14. $210 $200 $25 8 8   15. 12 months $47 12 $50 $600     16. 19 gallons $3.11 20 $3 $60     17. $7.99 $4.23 $16.82 $3.51 $20.12 $8 $4 $17 $4 $20 $53           18. $1.29 $6.86 $12.43 $25.62 $8.99 $1 $7 $12 $26 $9 $55           19. 95lb 127 lb 210 lb 100 100 200 400 lb       20. 16.1 lb 7.9 lb 21.4 lb 11.6 lb 3.7 lb 16 8 21 12 4 61 lb           21. 15% of $26.32 15% of $26 0.15 $26 $3.90     22. $400 $400 16 $23 $25   23. $595 $289 $120 $110 230 $600 $300 $100 $100 $200 $1300           24. Team A: 189 172 191 190 170 190 550       Team B: 183 229 167 180 230 170 580       580 550 30 lb   25. 11 8 $1.50 10 8 $1.50 10 $12 $120         26. 9 min, 55 sec/mi 26.2 mi 10 min 26 mi 260 min/mi;     260 min 1 4 hours 60 min 3  27. 599 Mexican pesos 600 $30 20.14 Mexican pesos / U.S. dollars 20  

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    4 Chapter 1: Critical Thinking Skills 28.             $973 6 $61 6 $97 6 $200 $970 6 $60 6 $100 6 $200 $970 $360 $600 $1200 $3130             29. 90 miles 30. 75 miles 31. a) 23% of 700 25% of 700 0.25 700 175     b) 12% of 700 10% of 700 0.10 700 70     c) 21% of 700 20% of 700 0.20 700 140     32. a) 18% of 2987 18% of 3000 0.18 3000 540     b) 42% of 2987 42% of 3000 0.42 3000 1260     c) 7% of 2987 7% of 3000 0.07 3000 210     33. a) 5 million b) 98 million c) 98 million 33 million 65 million   d) 19 million 79 million 84 million 65 million 33 million 280 million      34. a) 19% b) 25% c) 20% of 179 lb 20% of 180 0.2 180 36 lb     35. a) 85% b) 68% 53% 15%   c) 85% of 70 million acres = 59,500,000 acres d) No, since we are not given the area of each state. 36. a)         2 410 4 545 2 400 4 500 800 2000 2800 calories       b) Running:     4 920 4 900 3600 calories   Walking:     4 330 4 300 1200 calories   Difference: 3600 1200 2400 calories   c)           3 545 3 545 3 550 3 550 1650 1650 3300 calories per week 3300 calories per week 52 weeks 3000 50 150, 000 calories          37. 20 38. 25 39. 120 bananas 40. 100 grapes 41. 150  42. 315  43. 10% 44. 25% 45. 9 square units 46. 12 square units 47. 160 feet 48. 240 4(60) 240 in. or 20 ft 12   49. – 57. Answers will vary.

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    Section 1.3: Problem-Solving Procedures 5 58. Cost of one vitamin C tablet: $24.99 $25 $0.05 500 500   Cost of one fish oil tablet: $47.99 $48 $0.40 120 120   Cost of one vitamin D tablet: $17.99 $18 $0.10 180 180   Cost of one multivitamin tablet: $19.99 $20 $0.25 80 80   Roberto’s daily cost: 5 $0.05 4 $0.40 1 $0.10 1 $0.25 $1.40         59. There are 118 ridges around the edge. 60. a) Answers will vary. b) 11.6 days. There are 24 60 60 86, 400    seconds in a day, and 1, 000, 000 / 86, 400 11.5740.  62. Answers will vary. 63. Answers will vary. Section 1.3: Problem-Solving Procedures 1.   1 in. 4.25 in. 12 mi mi 12 4.25 51 mi x x x    2.   1 in. 22.4 in. 2.5 yd yd 1 2.5 22.4 56 yd x x x    3.   3 ft ft 1.2 ft 15.36 ft 3 15.36 1.2 46.03 1.2 1.2 1.2 46.03 38.4 ft 1.2 x x x x      4.   2 2 1 bag bags 4000 ft 35, 000 ft 4000 1 35, 000 4000 35, 000 4000 4000 35, 000 8.75 bags 4000 x x x x      5. 4 $113 $452 9.25% of $452 0.0925 $452 $41.81 $452 $41.81 $493.81        6. 2 $187 $374 9.5% of $374 0.095 $374 $35.53 $374 $35.53 $409.53        7. a) Entertainment/Miscellaneous: 19.1% of $1950 0.191 $1950 $372.45    Food: 12.7% of $1950 0.127 $1950 $247.65    $372.45 $247.65 $124.80   b) Housing: 34.4% of $1950 0.344 $1950 $670.80    Transportation: 16% of $1950 0.16 $1750 $312.00    $670.80 $312.00 $358.80   8. a) Business: 19% of 2,895, 000 0.19 2,895, 000 550, 050    Engineering: 5% of 2,895, 000 0.05 2,895, 000 144, 750    550, 050 144, 750 405,300 degrees  

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    6 Chapter 1: Critical Thinking Skills 8. (continued) b) Health Professions: 11% of 2,895, 000 0.11 2,895, 000 318, 450    Psychology: 6% of 2,895, 000 0.06 2,895, 000 173, 700    318, 450 173, 700 144, 750 degrees   9. 43 rides $2.00 per ride $86.00;   In order for the cost of rides with the $84.50 MetroCard to be less than the cost of the rides without the CharlieCard, Marcelo would have to take 43 bus rides per month. Note that $84.50 $1.97 per ride. 43rides  10. 45 rides $2.75 per ride $123.75;   In order for the cost of rides with the $121.50 MetroCard to be less than the cost of the rides without the MetroCard, Karissa would have to take 45 subway rides per month. Note that $121.50 $2.70 per ride 45 rides  11.   $250 $130 18 $250 $2340 $2590     Savings: $2590 $2500 $90   12. $349.72 $32.39(4) $349.72 129.56 $220.16     13. 15-year mortgage: $887.63(12)(15) $159, 773.40  30-year mortgage: $572.90(12)(30) $206, 244.00  Savings: $206, 244.00 $159, 773.40 $46, 470.60   14. Points needed for 80 average: 80(5) 400 points  Wallace’s points so far: 79 93 91 68 331 points     Grade needed on fifth exam: 400 331 69   15. a) 10 10 10 10 10, 000     b) 1 in 10,000 16. a) 460 18.4 min 25  b) 1550 31 min 50  c) 1400 40 min 35  d) 1550 2200 3750 47 min 80 80 80    17. 38, 687.0 mi 38, 451.4 mi 235.6 mi;   235.6 mi 18.7 mpg 12.6 gal  18. a) 40 $8.50 52 $17, 680    b) Each week he makes 40 $8.50 $340,   it will take him $1275 3.75 weeks. $340  19. By mail:   $52.80 $5.60 $8.56 4 $66.96 4 $267.84       Tire store: $324 0.08 $324 $324 $25.92 $349.92      Savings: $349.92 $267.84 $82.08   20.   $1750 $50 15 $1750 $750 $1000     and $1000 25 hours $40 

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    Section 1.3: Problem-Solving Procedures 7 21. 15,000 ft  3000 ft = 12,000 ft decrease in elevation. Temperature increases 2.4 F  for every 1000 ft decrease in elevation. 6 F 28.8 F 22.8 F       and 6 F 28.8 F 22.8 F;       The precipitation at the airport will be snow. 22. a)   $620 0.12 $74.40  b)   $1200 0.22 $264  c) The store lost $1200 $1000 $200   on the purchase, so the store’s profit is $264 $200 $64.   23. a) Since $876 is less than 10% $9525 $952.50,   Shenile’s tax was 10% of her taxable income. Her taxable income was $876 $8760. 0.10  b) Since $2017.50 is greater than $952.50 and less than $4453.50, Logan’s taxable income was in the 12% bracket. Since $2017.50 $962.50 $1065   was 12% of his taxable income above $9525, he made an additional $1065 $8875. 0.12  His taxable income was $9625 $8875 $18, 400.   24. a) Since $4541.50 is greater than $4453.50 and less than $14,089.50, Lewis’ taxable income was in the 22% bracket. Since $4541.50 $4453.50 $88   was 22% of his taxable income above $38,700, he made an additional $88 $400. 0.22  His taxable income was $38, 700 $400 $39,100.   b) Since $14,593.50.50 is greater than $14,089.50 and less than $32,089, Leticia’s taxable income was in the 24% bracket. Since $14,593.50 $14, 089.50 $504   was 24% of his taxable income above $82,500, she made an additional $504 $2100. 0.24  Her taxable income was $82,500 $2100 $84, 600.   25. a) 1 60 24 365 525, 600 oz     and 525, 600 oz 4106.25 gal 128  b) 4106.25 $11.20 4.10625 $11.20 $45.99 1000     26. a) 3 0.1 60 60 24 365 3,153, 600 cm      b) 3 3 Volume of basin (30 cm)(20 cm)(20 cm) 12, 000 cm 1.4; Daily water loss 0.1 60 60 24 8640 cm       It would take about 1.4 days. 27. a) 20, 000 20, 000 961.538 925.926 35.612 35.61 gal 20.8 21.6      b) 35.61 $3.00 $106.83   c) 140, 000, 000 35.61 4,985, 400, 000 gal   28. a) Parking: $30 6 $180   Tax: 9.5% of $180 0.095 $180 $17.10    Total: $180 $17.10 $197.10   b) Parking: $17.95 6 $107.70   Tax: 8.75% of $107.70 0.0875 $107.70 $9.42    Total: $107.70 $9.42 $117.12   c) She can save $197.10 $117.12 $79.98.  

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    8 Chapter 1: Critical Thinking Skills 29. Cost after 1 year: $999 0.02($999) $999 $19.98 $1018.98     Cost after second year: $1018.98 0.02($1018.98) $1018.98 $20.38 $1039.36     30. Value after first year: $1000 0.10($1000) $1000 $100 $1100     Value after second year:   $1100 0.10 $1100 $1100 $110 $990     $990 is less than the initial investment of $1000. 31. After paying the $100 deductible, Yungchen must pay 20% of the cost of x-rays. First x-ray:   $100 0.20 $620 $100 $124 $224     Second x-ray:   0.20 $980 $196  Total: $224 $196 $420   32. $3000 is the difference between one-fourth of the cost and one-fifth of the cost. 1 1 1 4 5 20   and 20 $3000 $60, 000   33. a) water/milk: 3(1) 3  cups salt: 1 3 3 8 8        tsp Cream of wheat:   3 3 9  tbsp 9 16  cup (because 16 tbsp = 1 cup) b) water/milk: 3 23 2 3 23 7 4 4 2 cups 2 2 8 8     salt: 1 1 3 3 4 2 4 tsp 2 2 8    cream of wheat: 1 3 5 5 2 4 4 cups =5 tbsp 2 2 8    c) water/milk: 3 15 4 11 3 3 1 2 4 4 4 4 4      cups salt: 1 1 4 1 3 2 8 8 8 8     tsp cream of wheat: 3 3 12 3 9 4 16 16 16 16     cup = 9 tbsp d) Differences exist in water/milk because the amount for 4 servings is not twice that for 2 servings. Differences also exist in Cream of Wheat because 1 2 cup is not twice 3 tbsp.

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    Section 1.3: Problem-Solving Procedures 9 34. a) rice:   1 4 2 2  cups water:     1 4 16 1 1 4 4 5 3 3 3 3    cups salt:   1 4 1 4  tsp butter/margarine:   1 4 4  tsp b) rice:   1 2 2  cups water:     1 9 18 2 1 2 2 2 4 4 4 4 4 4 2     cups salt:   1 2 1 2  tsp butter/margarine:   2 2 4  tsp c) rice: 1 1 1 3 4 1 2 2 2 2 2 2      cups water: 1 1 4 10 14 2 1 3 4 3 3 3 3 3 3      cups salt: 1 3 4 1 4 4 4    tsp butter/margarine: 1 tsp 1 tbsp 1 tsp 3 tsp 4 tsp     d) rice: 3 1 2 cups   1 24 9 15 3 water: 6 2 3 cups 4 4 4 4 4      1 1 salt: 1 1 tsp 2 2     butter/margarine: 2 tbsp 2 tsp 2 3tsp 2 tsp 6 tsp 2 tsp 4 tsp       e) Differences exist in water because the amount for 4 servings is not twice that for 2 servings. 35. a) 20 DVDs 12 DVDs Total Number of DVDs 1 1 20 12 32   0 2 12 12 24   b) $240 $180 $420   36. Mark will win. 37. 2 1 ft 12 in. 12 in. 144 square inches    38. 3 1 ft 12 in. 12 in. 12 in. 1728 cubic inches     39. Area of original rectangle: lw Area of new rectangle: (2 )(2 ) 4( ) l w lw  Thus, if the length and width of a rectangle are doubled, the area is 4 times as large.

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    10 Chapter 1: Critical Thinking Skills 40. 2 20 ft 20 ft = 400 ft ;  2 5ft 5ft = 25 ft ;  2 2 400 ft 16squares 25ft  41. Volume of original cube: lwh Volume of new cube: (2 )(2 )(2 ) 8( ) l w h lwh  Thus, if the length, width, and height of a cube are doubled, the volume is 8 times as large. 42. 11 ft is one-sixth of the pole, so the length is 6 11 ft 66 ft.   43.   10 pieces 1000 pieces $10 1000 10 10 1000 100 1000 1000 100 $0.10 10¢ 1000 x x x x       44. Left side Right side 1( 6) 6 1(2) 2 2( 2) 4 1(3) 3 (6) 6 6 ( 4) 10 2 3 6 11                  Place it at –1, so the left side would total 10 ( 1) 1.      45. You have three ties, each a different color. 46. There are 10 palindromes: 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992. 47. a) refresh b) workout 48. Answers will vary. 49. 50. Eight pieces 51. 52. 53. 8 6 2 4 20; 3 7 5 1 16; 10 14 12 8 44             The sum of the four corner entries is 4 times the number in the center of the middle row. 54. 15,12,33; Multiply the number in the center of the middle row by 3. 55. 45,36,99; Multiply the number in the center of the middle row by 9. 56. 35 15 20 cubes   57. 3 2 1 6 ways    58. Each salesperson shakes hands with four people.

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