Document Sample

Thinking Mathematically MATH1101 Comprehensive Mathematics Homework Solutions Chapter 6 Chapter 6, Section 1 1. 5x + 7 2. 9x + 6 3. -7x – 5 4. -6x – 13 5. x2 + 4 54 + 7 95 + 6 (-7)(-4) – 5 (-6)(-3) – 13 55 + 4 20+7 45 + 6 28 – 5 18 – 13 25 + 4 27 51 23 5 29 6. x2 + 9 7. x2 - 6 8. x2 - 11 9. x2 + 4x 10. x2 + 6x 33 + 9 (-2)(-2) - 6 (-3)(-3)-11 1010 + 410 99 + 69 9+9 4-6 9-11 100+40 81 + 54 18 -2 -2 140 135 Chapter 6, Section 1 35. 7x + 10x (7+10)x distributive law 17x addition 36. 5x + 13x (5+13)x distributive law 18x addition Chapter 6, Section 1 37. 5x2 - 8x2 (5 - 8)x2 distributive law -3x2 addition 38. 7x2 - 10x2 (7 - 10)x2 distributive law -3x2 addition Chapter 6, Section 1 39. 3(x + 5) 3x +35 distributive law 3x + 15 multiplication 40. 4(x + 6) 4x +46 distributive law 4x + 24 multiplication Chapter 6, Section 1 41. 4(2x - 3) 42x - 43 distributive law 8x - 12 multiplication 42. 3(4x - 5) 34x - 35 distributive law 12x - 15 multiplication Chapter 6, Section 1 61. The difference between a and b: a – b 5x – 2x which is equal to 3x. 62. 6x – (-2x) which equals 6x + 2x = 8x. 63. 8x – (3x + 6) which equals 8x + (-3x – 6) = 5x – 6. 64. 8 – 3(x + 6) which equals 8 + (-3x – 18) = -3x - 10 Chapter 6, Section 2 1. x–7=3 since 7 is subtracted from x check: 10 – 7 = 3 x – 7 + 7 = 3 + 7 add 7 to both sides 3=3 x + 0 = 10 perform additions x = 10 2. x – 3 = -17 since 3 is subtracted from x check: -14 – 3 = -17 x – 3 + 3 = -17 + 3 add 3 to both sides -17 = -17 x + 0 = -14 perform additions x = -14 Chapter 6, Section 2 3. x + 5 = -12 since 5 is added to x check:-17 + 5 = -12 x + 5 - 5 = -12 - 5 subtract 5 from both sides 12 = 12 x + 0 = -17 perform subtraction x = -17 4. x + 12 = -14 since 12 is added to x check:-26 + 12 = -14 x + 12 - 12 = -14 - 12 subtract 5 from both sides -14 = -14 x + 0 = -26 perform subtraction x = -26 Chapter 6, Section 2 x 12 5. =4 since x is divided by 3 check: =4 3 3 x × 3= 4 × 3 multiply both sides by 3 4=4 3 x = 12 perform multiplication x 15 6. 5 =3 since x is divided by 5 check: =3 5 x 5 × 5= 3 × 5 multiply both sides by 5 3=3 x = 15 perform multiplication Chapter 6, Section 2 7. 5x = 45 since x is multiplied by 5 check: 5 × 9= 45 5x/5 = 45/5 divide both sides by 5 45 = 45 x =9 perform division 8. 6x = 18 since x is multiplied by 6 check: 6 × 3= 18 6x/6 = 18/6 divide both sides by 6 18 = 18 x =3 perform division Chapter 6, Section 2 9. 8x = -24 since x is multiplied by 8 check: 8 × -3= -24 8x/8 = -24/8 divide both sides by 8 -24 = -24 x = -3 perform division 10. 5x = -25 since x is multiplied by 5 check: 5 × -5 = -25 5x/5 = -25/5 divide both sides by 5 -25 = -25 x = -5 perform division Chapter 6, Section 2 x x 5 check: 43. Get rid of the 3 denominator by 3 2 6 1 1 2 3 23 5 multiplying by 3 x x 5 3 2 6 6 6 6 3 3 3 2 6 3 x 15 Get rid of the 2 denominator by x 2 6 multiplying by 2 3x 15 2 x 2 2 6 30 2x 3x 5 6 5x 5 x 1 Chapter 6, Section 2 x x check: 44. 1 Get rid of the 4 denominator by 4 5 20 20 multiplying by 4 1 x 4x 4 5 4 1 4 5 51 4 4x Get rid of the 5 denominator by 44 x4 5 multiplying by 5 4x 5 x 4 5 5 5 x 20 4 x Add 20 to both sides 5 x 4 x 20 5 x 4 x 4 x 20 4 x Subtract 4x from both sides x 20 Chapter 6, Section 2 x x Get rid of the 2 denominator by check: 24 20 24 45. 20 2 3 multiplying by 2 2 3 x x 12 20 8 2 2 20 2 3 12 12 2x x 40 Get rid of the 3 denominator by 3 multiplying by 3 2x 3 x 3 40 3 3 x 120 2 x Add 2x to both sides 3 x 2 x 120 2 x 2 x 5 x 120 Divide both sides by 5 x 24 Chapter 6, Section 2 x 1 x Get rid of the 5 denominator by 46. check: 15 1 15 5 2 6 multiplying by 5 x 1 5x 5 2 6 5 15 1 5 5 2 6 5 5 x Get rid of the 6 denominator by 5 2 2 x 1 5 2 6 multiplying by 6 3 2 2 5 6 x 5x 6 1 5 2 2 2 2 30 6x 6 x 15 5 x Add 15 to both sides 5 5 2 2 2 6 x 5 x 15 6 x 5 x 5 x 15 5 x Subtract 5x from both sides x 15 Chapter 6, Section 2 61. A= ½(a + b) Multiply both sides by 2 2A = a + b Subtract b from both sides 2A – b = a to isolate a This is the formula for the average of 62. A= ½(a + b) Multiply both sides by 2 two numbers. 2A = a + b Subtract a from both sides 2A – a = b to isolate b Chapter 6, Section 2 63. S = P + Prt Subtract P from both sides S – P = Prt Divide both sides by P SP rt Divide both sides by t P SP This is the formula for r compound interest that Pt we will discover in Chapter 8. Chapter 6, Section 2 64. S = P + Prt Subtract P from both sides S – P = Prt Divide both sides by P SP rt Divide both sides by r P SP This is the formula for t compound interest that Pr we will discover in Chapter 8. Chapter 6, Section 3 1. Five times a number: 5x decreased by 4: - 4 5x – 4 = 26 5x = 26 + 4 = 30 x=6 When five times 6 is decreased by 4, 30 is decreased by 4, which IS 26. Chapter 6, Section 3 2. Two times a number: 2x decreased by 3: - 3 2x – 3 = 11 2x = 11 + 3 = 14 x=7 When twp times 7 is decreased by 3, 14 is decreased by 3, which IS 11. Chapter 6, Section 3 3. One number exceeds another by 26: x = y + 26 The sum of the numbers is 64: x + y = 64 x + y = 64 (y + 26) + y = 64 2y + 26 = 64 2y = 38 y = 19 x = y + 26 = 19 + 26 = 45 45 does exceed 19 by 26, and the sum of 19 and 45 is 64. Chapter 6, Section 3 4. One number exceeds another by 24: x = y + 24 The sum of the numbers is 58: x + y = 58 x + y = 58 (y + 24) + y = 58 2y + 24 = 58 2y = 34 y = 17 x = y + 24 = 17 + 24 = 41 41 does exceed 17 by 24, and the sum of 17 and 41 is 58. Chapter 6, Section 3 15. Plan A: 40 + 25m, where m is the number of months. Plan B: 15 + 30m, where m is the number of months. These will be equal when 40 + 25m = 15 + 30m. 40 + 25m = 15 + 30m 40 – 15 = 30m – 25m 25 = 5m m = 5. Plans even out at 5 months (for 40 + 25×5 = $165) Note that 15 + 30×5 = 15 + 150 = $165 as well. Chapter 6, Section 3 16. Store A: 9r where r is the number of rentals Plan B: 4r + 50. (Since they charge a membership of $50) These will be equal when 9r = 4r + 50. 9r = 4r + 50 9r – 4r = 50 5r = 50 r = 10. Cost evens out after 10 rentals (for 9×10 = $90) Note that 4×10 + 50 = 40 + 50 = $90 as well. Chapter 6, Section 3 17. With Coupon Book: 15 + .75x, where x is the number of times used. Without Coupon Book: 1.25x, where x is the number of times used. These will be equal when 15 + .75x = 1.25x. 15 + .75x = 1.25x 15 = 1.25x – .75x 15 = 0.5x x = 30. Plans even out at 30 uses (for 15 + .75×30 = $15 + 22.50 = $37.50) Note that 1.25×30 = $37.50 as well. Chapter 6, Section 3 18. With Coupon Book: 30 + 3.50x, where x is the number of times used. Without Coupon Book: 5.00x, where x is the number of times used. These will be equal when 30 + 3.50x = 5.00x. 30 + 3.50x = 5.00x 30 = 5.00x – 3.50x 30 = 1.50x x = 20. Plans even out at 20 uses (for 30 + 3.50×20 = $30 + $70 = $100) Note that 5.00×20 = $100 as well. Chapter 6, Section 3 21. Customer was charged $448. This consisted of parts and labor. Parts were $63. Labor was $35x where x is the number of hours. So $448 = $63 + $35x. 448 = 63 + 35x 448 – 63 = 385 = 63 + 35x – 63 385 = 35x x = 385/35 = 11. Answer: 11 hours of labor. Chapter 6, Section 3 22. Customer was charged $1603. This consisted of parts and labor. Parts were $532. Labor was $63x where x is the number of hours. So $1603 = $532 + $63x. 1603 = 532 + 63x 1603 – 532 = 1071 = 532 + 63x – 532 1071 = 63x x = 1071/63 = 17. Answer: 17 hours of labor. Chapter 6, Section 3 23. The job pays $33,150. Part of this is a holiday bonus and the rest is salary, which is paid 2 times a month. So in a year, there are 24 paychecks. Each paycheck is 1/24th of the annual salary (minus the bonus) $33,150 = $750 + 24x 33150 = 750 + 24x 32400 = 24x 1350 = x. Each paycheck, therefore, is for $1,350. (Multiply 1350 by 24 and add 750 and see if that equals 33150!) Chapter 6, Section 3 24. There are three vertical pieces and four horizontal pieces (even though two of these will have to be cut in half.) If x is the height, the length is 3x. So 3x + 4(3x) = 60 3x + 12x = 60. 15x = 60 x = 4, so the height is four feet. The length (three times the height) is twelve feet.) Chapter 6, Section 4 1. 24 12 x 7 12x = 247 = 168 x = 168 12 = 14 2. 56 8 x 7 8x = 567 = 392 x = 392 8 = 49 Chapter 6, Section 4 3. x 18 6 4 4x = 186 = 108 x = 108 4 = 27 4. x 3 32 24 24x = 323 = 96 x = 96 24 = 4 Chapter 6, Section 4 5. x 3 , rewrite as x 3 be careful with the minus sign 3 4 3 4 here. A negative fraction means 4x = -33 = -9 that only the numerator is x = -9 4 = -2¼ negative. 6. x 1 x 1 , rewrite as 2 5 2 5 5x = -12 = -2 x = -2 5 = -2/5 Chapter 6, Section 4 23. $725 x $65 , 000 $100 , 000 65000x = 725 100000 = 72500000 x = 72500000 65000 x =$1115.38 Chapter 6, Section 4 26. 50 27 x 108 27x = 50 108 = 5400 x = 5400 27 x = 200 There are approximately 200 bass in the lake.

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 42 |

posted: | 8/13/2011 |

language: | English |

pages: | 37 |

OTHER DOCS BY cuiliqing

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.