{"id":23,"date":"2025-01-02T23:02:27","date_gmt":"2025-01-02T23:02:27","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/general-problem-solving-get-stronger-answer-key\/"},"modified":"2025-01-02T23:02:27","modified_gmt":"2025-01-02T23:02:27","slug":"general-problem-solving-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/general-problem-solving-get-stronger-answer-key\/","title":{"raw":"General Problem Solving: Get Stronger Answer Key","rendered":"General Problem Solving: Get Stronger Answer Key"},"content":{"raw":"\n
    \n \t
  1. [latex]18 \/ 230 = 0.07826[\/latex] = about [latex]7.8\\%[\/latex]<\/li>\n \t
  2. <\/li>\n \t
  3. [latex]\u20ac 250(0.23)=\u20ac 57.50[\/latex] in VAT<\/li>\n \t
  4. <\/li>\n \t
  5. [latex]\\$ 15000(5.57)=\\$ 83,550[\/latex] in VAT<\/li>\n \t
  6. <\/li>\n \t
  7. absolute increase: [latex]1050[\/latex]. Relative: [latex]1050[\/latex] \/ [latex]3250[\/latex] = [latex]0.323[\/latex] = [latex]32.3[\/latex] increase in VAT<\/li>\n \t
  8. <\/li>\n \t
  9. a. [latex]2200\u22122200(0.15)=2200(0.85)=1$1870[\/latex]\nb. Yes, their goal was to decrease by at least [latex]15\\%[\/latex]. They exceeded their goal.<\/li>\n \t
  10. <\/li>\n \t
  11. Dropping by [latex]6\\%[\/latex] is the same as keeping [latex]94\\%[\/latex]. [latex] a(0.94)=300.  a=319.15[\/latex].\n<\/span><\/span>Attendance was about [latex]319[\/latex] before the drop.<\/span><\/li>\n \t
  12. <\/li>\n \t
  13. a) Kaplan\u2019s enrollment was [latex]64.3\\%[\/latex] larger than Walden\u2019s. [latex]30510[\/latex]\nb) Walden\u2019s enrollment was [latex]39.1\\%[\/latex] smaller than Kaplan\u2019s.\nc) Walden\u2019s enrollment was [latex]60.9\\%[\/latex] of Kaplan\u2019s.<\/li>\n \t
  14. <\/li>\n \t
  15. If the original price was [latex]$100[\/latex], <\/span>the basic clearance price would be [latex]100$ - $100(0.60) = $40[\/latex].\nThe additional markdown would bring it to [latex]$40 - $40(0.30) = $28[\/latex]. This is [latex]28\\%[\/latex]\nof the original price.<\/li>\n \t
  16. <\/li>\n \t
  17. These are not comparable; \u201ca\u201d is using a base of all Americans and is talking about health insurance from any source, while \u201cb\u201d is using a base of adults and is talking specifically about health insurance provided by employers.<\/li>\n \t
  18. <\/li>\n \t
  19. <\/li>\n \t
  20. <\/li>\n \t
  21. These statements are equivalent, if we assume the claim in \u201ca\u201d is a percentage point increase, not a relative change. Certainly these messages are phrased to convey different opinions of the levy. We are told the new rate will be [latex]$9.33[\/latex] per [latex]$1000[\/latex], which is [latex]0.933\\%[\/latex] tax rate. If the original rate was [latex]0.833\\%[\/latex] ([latex]0.1[\/latex] percentage point lower), then this would indeed be a [latex]12\\%[\/latex] relative increase.<\/li>\n \t
  22. <\/li>\n \t
  23. <\/span>[latex]20\\%[\/latex] <\/span>of [latex]30\\%[\/latex] is [latex]30\\%(0.20)=6\\%[\/latex], a [latex]6[\/latex] percentage point decrease.<\/li>\n \t
  24. <\/li>\n \t
  25. Probably not, unless the final is worth [latex]50\\%[\/latex] of the overall class grade. If the final was worth [latex]25\\%[\/latex] of the overall grade, then a [latex]100\\%[\/latex] would only raise her average to [latex]77.5\\%[\/latex]<\/li>\n \t
  26. <\/li>\n \t
  27. <\/span>[latex]$4\/10[\/latex] <\/span><\/span>pounds [latex]$0.40[\/latex] <\/span>per pound (or [latex]10[\/latex] pounds\/\\ [latex]$4 = 2.5[\/latex] pounds per dollar)<\/li>\n \t
  28. <\/li>\n \t
  29. x <\/span>= <\/span>[latex]15[\/latex]<\/span><\/span><\/li>\n \t
  30. <\/li>\n \t
  31. [latex]2.5[\/latex] cups<\/li>\n \t
  32. <\/li>\n \t
  33. [latex]74[\/latex] turbines<\/li>\n \t
  34. <\/li>\n \t
  35. [latex]96[\/latex] inches<\/li>\n \t
  36. <\/li>\n \t
  37. [latex]$6000[\/latex]<\/li>\n \t
  38. <\/li>\n \t
  39. [latex]55.6[\/latex] meters<\/li>\n \t
  40. <\/li>\n \t
  41. <\/li>\n \t
  42. <\/li>\n \t
  43. The population density of the US is [latex]84[\/latex] people per square mile. The density of India is about [latex]933[\/latex] people per square mile. The density of India is about [latex]11[\/latex] times greater than that of the U.S.<\/li>\n \t
  44. <\/li>\n \t
  45. <\/li>\n \t
  46. <\/li>\n \t
  47. <\/li>\n \t
  48. <\/li>\n \t
  49. The oil in the spill could produce [latex]93.1[\/latex] million gallons of gasoline. Each car uses about [latex]600[\/latex] gallons a year. That would fuel [latex]155,167[\/latex] cars for a year.<\/li>\n \t
  50. <\/li>\n \t
  51. <\/li>\n \t
  52. <\/li>\n \t
  53. An answer around [latex]100-300[\/latex] gallons would be reasonable<\/li>\n \t
  54. <\/li>\n \t
  55. <\/li>\n \t
  56. <\/li>\n \t
  57. [latex]156[\/latex] million miles<\/li>\n \t
  58. <\/li>\n \t
  59. The time it takes the light to reach you is so tiny for any reasonable distance that we can safely ignore it. [latex]750[\/latex] miles\/hr is about [latex]0.21[\/latex] miles\/sec. If the sound takes [latex]4[\/latex] seconds to reach you, the lightning is about [latex]0.84[\/latex] miles away. In general, the lightning will be [latex]0.21n[\/latex] <\/span>miles away, which is often approximated by dividing the number of seconds by [latex]5[\/latex]<\/li>\n \t
  60. <\/li>\n \t
  61. About [latex]8.2[\/latex] minutes<\/li>\n \t
  62. <\/li>\n \t
  63. Four cubic yards (or [latex]3.7[\/latex] if they sell partial cubic yards)<\/li>\n<\/ol>\n","rendered":"
      \n
    1. [latex]18 \/ 230 = 0.07826[\/latex] = about [latex]7.8\\%[\/latex]<\/li>\n
    2. <\/li>\n
    3. [latex]\u20ac 250(0.23)=\u20ac 57.50[\/latex] in VAT<\/li>\n
    4. <\/li>\n
    5. [latex]\\$ 15000(5.57)=\\$ 83,550[\/latex] in VAT<\/li>\n
    6. <\/li>\n
    7. absolute increase: [latex]1050[\/latex]. Relative: [latex]1050[\/latex] \/ [latex]3250[\/latex] = [latex]0.323[\/latex] = [latex]32.3[\/latex] increase in VAT<\/li>\n
    8. <\/li>\n
    9. a. [latex]2200\u22122200(0.15)=2200(0.85)=1$1870[\/latex]
      \nb. Yes, their goal was to decrease by at least [latex]15\\%[\/latex]. They exceeded their goal.<\/li>\n
    10. <\/li>\n
    11. Dropping by [latex]6\\%[\/latex] is the same as keeping [latex]94\\%[\/latex]. [latex]a(0.94)=300.  a=319.15[\/latex].
      \n<\/span><\/span>Attendance was about [latex]319[\/latex] before the drop.<\/span><\/li>\n
    12. <\/li>\n
    13. a) Kaplan\u2019s enrollment was [latex]64.3\\%[\/latex] larger than Walden\u2019s. [latex]30510[\/latex]
      \nb) Walden\u2019s enrollment was [latex]39.1\\%[\/latex] smaller than Kaplan\u2019s.
      \nc) Walden\u2019s enrollment was [latex]60.9\\%[\/latex] of Kaplan\u2019s.<\/li>\n
    14. <\/li>\n
    15. If the original price was [latex]$100[\/latex], <\/span>the basic clearance price would be [latex]100$ - $100(0.60) = $40[\/latex].
      \nThe additional markdown would bring it to [latex]$40 - $40(0.30) = $28[\/latex]. This is [latex]28\\%[\/latex]
      \nof the original price.<\/li>\n
    16. <\/li>\n
    17. These are not comparable; \u201ca\u201d is using a base of all Americans and is talking about health insurance from any source, while \u201cb\u201d is using a base of adults and is talking specifically about health insurance provided by employers.<\/li>\n
    18. <\/li>\n
    19. <\/li>\n
    20. <\/li>\n
    21. These statements are equivalent, if we assume the claim in \u201ca\u201d is a percentage point increase, not a relative change. Certainly these messages are phrased to convey different opinions of the levy. We are told the new rate will be [latex]$9.33[\/latex] per [latex]$1000[\/latex], which is [latex]0.933\\%[\/latex] tax rate. If the original rate was [latex]0.833\\%[\/latex] ([latex]0.1[\/latex] percentage point lower), then this would indeed be a [latex]12\\%[\/latex] relative increase.<\/li>\n
    22. <\/li>\n
    23. <\/span>[latex]20\\%[\/latex] <\/span>of [latex]30\\%[\/latex] is [latex]30\\%(0.20)=6\\%[\/latex], a [latex]6[\/latex] percentage point decrease.<\/li>\n
    24. <\/li>\n
    25. Probably not, unless the final is worth [latex]50\\%[\/latex] of the overall class grade. If the final was worth [latex]25\\%[\/latex] of the overall grade, then a [latex]100\\%[\/latex] would only raise her average to [latex]77.5\\%[\/latex]<\/li>\n
    26. <\/li>\n
    27. <\/span>[latex]$4\/10[\/latex] <\/span><\/span>pounds [latex]$0.40[\/latex] <\/span>per pound (or [latex]10[\/latex] pounds\/\\ [latex]$4 = 2.5[\/latex] pounds per dollar)<\/li>\n
    28. <\/li>\n
    29. x <\/span>= <\/span>[latex]15[\/latex]<\/span><\/span><\/li>\n
    30. <\/li>\n
    31. [latex]2.5[\/latex] cups<\/li>\n
    32. <\/li>\n
    33. [latex]74[\/latex] turbines<\/li>\n
    34. <\/li>\n
    35. [latex]96[\/latex] inches<\/li>\n
    36. <\/li>\n
    37. [latex]$6000[\/latex]<\/li>\n
    38. <\/li>\n
    39. [latex]55.6[\/latex] meters<\/li>\n
    40. <\/li>\n
    41. <\/li>\n
    42. <\/li>\n
    43. The population density of the US is [latex]84[\/latex] people per square mile. The density of India is about [latex]933[\/latex] people per square mile. The density of India is about [latex]11[\/latex] times greater than that of the U.S.<\/li>\n
    44. <\/li>\n
    45. <\/li>\n
    46. <\/li>\n
    47. <\/li>\n
    48. <\/li>\n
    49. The oil in the spill could produce [latex]93.1[\/latex] million gallons of gasoline. Each car uses about [latex]600[\/latex] gallons a year. That would fuel [latex]155,167[\/latex] cars for a year.<\/li>\n
    50. <\/li>\n
    51. <\/li>\n
    52. <\/li>\n
    53. An answer around [latex]100-300[\/latex] gallons would be reasonable<\/li>\n
    54. <\/li>\n
    55. <\/li>\n
    56. <\/li>\n
    57. [latex]156[\/latex] million miles<\/li>\n
    58. <\/li>\n
    59. The time it takes the light to reach you is so tiny for any reasonable distance that we can safely ignore it. [latex]750[\/latex] miles\/hr is about [latex]0.21[\/latex] miles\/sec. If the sound takes [latex]4[\/latex] seconds to reach you, the lightning is about [latex]0.84[\/latex] miles away. In general, the lightning will be [latex]0.21n[\/latex] <\/span>miles away, which is often approximated by dividing the number of seconds by [latex]5[\/latex]<\/li>\n
    60. <\/li>\n
    61. About [latex]8.2[\/latex] minutes<\/li>\n
    62. <\/li>\n
    63. Four cubic yards (or [latex]3.7[\/latex] if they sell partial cubic yards)<\/li>\n<\/ol>\n","protected":false},"author":6,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":3,"module-header":"","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/23"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/23\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/23\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=23"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=23"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=23"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=23"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}