Worked-out Problems

More documents

Recommendations

Info

$Unit 2- Measurements, Math, and the Mole$

Chapter 3 continued 30. 3 ≤ 2x 4 4 4(3) ≤ 4 p 2x 4 4 12 ≤ 2x 4 12 4 ≤ 2x 4 4 16 ≤ 2x 16 2x ≤ 2 2 12 10 8 ≤ x, orx ≥ 8 8 31. Let x the number of sets of cards. Cost: Cost per Cards Number Table p p card in a set of sets cost 0.50 p 12 p x 20 6x 20 Income: Price Number p 10.20x per set of sets 10.20x > 6x 20 10.20x 6x > 6x 20 6x 4.20x > 20 4 . 20x 20 > 4. 20 4 .20 x > 4.76 You must sell at least 5 sets of cards. 32. a. Let x the number of minutes. Monthly fee 6 4 2 Per minute charge Company A: 2 0.039x Company B: 0.049x 2 0.039x < 0.049x 2 0.039x 0.039x < 0.049x 0.039x 2 < 0.01x 2 0. 01 < 0 . 01x 0. 01 200 < x The cost of company A will be less than the cost of company B after more than 200 minutes. b. Company C: 1.95 0.044x 1.95 0.044x < 0.049x 1.95 0.044x 0.044x < 0.049x 0.044x 1.95 < 0.005x 1.95 < 0 . 005x 0 .005 0. 005 390 < x The cost of company C will be less than the cost of company B after more than 390 minutes. ––CONTINUED–– 102 Pre-Algebra Chapter 3 <strong>Worked</strong>-Out Solution Key 0 p Number of minutes 32. ––CONTINUED–– c. If you spend 150 minutes each month making long-distance calls, use company B. Cost using company A: $2 $.039(150) $7.85; Cost using company B: $.049(150) $7.35; Cost using company C: $1.95 $.044(150) $8.55 33. x ≥ 4 and x < 3, or all values between 4 and 3, including 4, but not 3. Sample answer: 2x 4 < 10 and 5 3x ≤ 17 2x 4 4 < 10 4 5 3x 5 ≤ 17 5 2x < 6 3x ≤ 12 2 x < 6 2 2 3x 12 ≥ 3 3 x < 3 and x ≥ 4 Both inequalities are true when x is less than 3 and greater than or equal to 4. 34. a. Let m the number of months that you and your friend have been members. b. Amount paid ($) m Amount you Amount your months have paid friend has paid y 600 500 400 300 200 100 1 $185 $140 2 $220 $180 3 $255 $220 4 $290 $260 5 $325 $300 6 $360 $340 7 $395 $380 8 $430 $420 9 $465 $460 10 $500 $500 11 $535 $540 12 $570 $580 Health Club Plans Me My friend 0 0 2 4 6 8 10 12m Number of months c. 11 months. Sample answer: After 10 months, the graphs share the same point, which means that the cost is the same. Then after that, the points corresponding to my cost go below those corresponding to my friend’s cost, which means that my plan is cheaper. ––CONTINUED–– Copyright © McDougal Littell/Houghton Mifflin Company All rights reserved.
Chapter 3 continued 34. ––CONTINUED–– d. Monthly fee p Number of months Membership fee Your health club: 150 35m Your friend’s health club: 100 40m 150 35m < 100 40m 150 35m 40m < 100 40m 40m 150 5m < 100 150 5m 150 < 100 150 5m < 50 5 m 5 > 50 5 m > 10 You will have paid less than your friend after more than 10 months. 3.6 Mixed Review (p. 153) 35. Point A is 1 unit to the right of the origin and 3 units up. So, the x-coordinate is 1 and the y-coordinate is 3. Point A is represented by the ordered pair (1, 3). 36. Point B is 3 units to the left of the origin and 1 unit down. So, the x-coordinate is 3 and the y-coordinate is 1. Point B is represented by the ordered pair (3, 1). 37. Point C is 3 units to the right of the origin. So, the x-coordinate is 3 and the y-coordinate is 0. Point C is represented by the ordered pair (3, 0). 38. Point D is 1 unit to the right of the origin and 3 units down. So, the x-coordinate is 1 and the y-coordinate is 3. Point D is represented by the ordered pair (1, 3). 39. Point E is 4 units to the left of the origin and 4 units up. So, the x-coordinate is 4 and the y-coordinate is 4. Point E is represented by the ordered pair (4, 4). 40. Point F is 1 unit to the left of the origin and 3 units up. So, the x-coordinate is 1 and the y-coordinate is 3. Point F is represented by the ordered pair (1, 3). 41. 13(2a 1) 13(2a) 13(1) 26a 13 42. 12 c 8 c 12 8 c 20 43. 5a a (5 1)a 6a 44. 3(x 4) 9 3x 12 9 3x 12 12 9 12 3x 3 3 x 3 3 3 x 1 Check: 3(x 4) 9 3(1 4) 9 9 9 ✓ 45. 4(2d 1) 28 8d 4 28 8d 4 4 28 4 8d 24 8 d 2 4 8 8 d 3 Check: 4(2d 1) 28 4[2(3) 1] 28 28 28 ✓ 46. 10 2(7 2x) 10 14 4x 10 14 14 4x 14 24 4x 24 4x 4 4 6 x Check: 10 2(7 2x) 10 2[7 2(6)] 10 10 ✓ 47. 3x 9 2x 7 3x 9 2x 2x 7 2x x 9 7 x 9 9 7 9 x 16 3.6 Standardized Test Practice (p. 153) 48. D; 7 6x ≥ 13 7 6x 7 ≥ 13 7 6x ≥ 6 6x 6 ≤ 6 6 x ≤ 1 49. I; 7x 3 < 7.5 7(3) 3 ? < 7.5 18 < 7.5 18 < 7.5, so 3 is a solution. Chapter 3 Review (pp. 154–157) 1. The value of a variable that, when substituted into an inequality, makes a true statement is a solution of an inequality. 2. Sample answer: 2x 3 ≤ 7 3. The inequalities of 2x < 2 and x < 1 are equivalent inequalities. Copyright © McDougal Littell/Houghton Mifflin Company All rights reserved. Chapter 3 Pre-Algebra 103 <strong>Worked</strong>-Out Solution Key
Page 1 and 2: Chapter 3 Chapter Opener Math in th
Page 3 and 4: Chapter 3 continued 11. 6 2m 8 12
Page 5 and 6: Chapter 3 continued 18. 2 x 4
Page 7 and 8: Chapter 3 continued 34. Your friend
Page 9 and 10: Chapter 3 continued 4. 3x 2x 25 5
Page 11 and 12: Chapter 3 continued 22. 5(2w 1) 2
Page 13 and 14: Chapter 3 continued 38. --CONTINUED
Page 15 and 16: Chapter 3 continued Brain Game --CO
Page 17 and 18: Chapter 3 continued 8. 5a 6 6a 3
Page 19 and 20: Chapter 3 continued 27. Let x the
Page 21 and 22: Chapter 3 continued 39. 0.75m 14
Page 23 and 24: Chapter 3 continued 6. w 18 7 2
Page 25 and 26: Chapter 3 continued 6. 5 < n 5 < 4,
Page 27 and 28: Chapter 3 continued 44. Sample answ
Page 29 and 30: Chapter 3 continued 11. (1) Let c
Page 31 and 32: Chapter 3 continued 42. 6.3a > 10.7
Page 33 and 34: Chapter 3 continued 2. 5x 12 < 8 S
Page 35: Chapter 3 continued 22. Let m the
Page 39 and 40: Chapter 3 continued 16. m 8 < 26 m
Page 41 and 42: Chapter 3 continued 5. 12 2m 5 1
Page 43 and 44: Chapter 3 continued Chapter 3 Stand
Page 45 and 46: Chapter 3 continued 18. --CONTINUED
Page 47: Chapter 3 continued 38. Let x numb

Worked-out Problems

Create successful ePaper yourself

Delete template?

Save as template?