General Problem Solving: Get Stronger Answer Key

  1. [latex]18 / 230 = 0.07826[/latex] = about [latex]7.8\%[/latex]
  3. [latex]€ 250(0.23)=€ 57.50[/latex] in VAT
  5. [latex]\$ 15000(5.57)=\$ 83,550[/latex] in VAT
  7. absolute increase: [latex]1050[/latex]. Relative: [latex]1050[/latex] / [latex]3250[/latex] = [latex]0.323[/latex] = [latex]32.3[/latex] increase in VAT
  9. a. [latex]2200−2200(0.15)=2200(0.85)=1$1870[/latex]
    b. Yes, their goal was to decrease by at least [latex]15\%[/latex]. They exceeded their goal.
  11. Dropping by [latex]6\%[/latex] is the same as keeping [latex]94\%[/latex]. [latex]a(0.94)=300.  a=319.15[/latex].
    Attendance was about [latex]319[/latex] before the drop.
  13. a) Kaplan’s enrollment was [latex]64.3\%[/latex] larger than Walden’s. [latex]30510[/latex]
    b) Walden’s enrollment was [latex]39.1\%[/latex] smaller than Kaplan’s.
    c) Walden’s enrollment was [latex]60.9\%[/latex] of Kaplan’s.
  15. If the original price was [latex]$100[/latex], the basic clearance price would be [latex]100$ - $100(0.60) = $40[/latex].
    The additional markdown would bring it to [latex]$40 - $40(0.30) = $28[/latex]. This is [latex]28\%[/latex]
    of the original price.
  17. These are not comparable; “a” is using a base of all Americans and is talking about health insurance from any source, while “b” is using a base of adults and is talking specifically about health insurance provided by employers.
  21. These statements are equivalent, if we assume the claim in “a” 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.
  23. [latex]20\%[/latex] of [latex]30\%[/latex] is [latex]30\%(0.20)=6\%[/latex], a [latex]6[/latex] percentage point decrease.
  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]
  27. [latex]$4/10[/latex] pounds [latex]$0.40[/latex] per pound (or [latex]10[/latex] pounds/\ [latex]$4 = 2.5[/latex] pounds per dollar)
  29. x = [latex]15[/latex]
  31. [latex]2.5[/latex] cups
  33. [latex]74[/latex] turbines
  35. [latex]96[/latex] inches
  37. [latex]$6000[/latex]
  39. [latex]55.6[/latex] meters
  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.
  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.
  53. An answer around [latex]100-300[/latex] gallons would be reasonable
  57. [latex]156[/latex] million miles
  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] miles away, which is often approximated by dividing the number of seconds by [latex]5[/latex]
  61. About [latex]8.2[/latex] minutes
  63. Four cubic yards (or [latex]3.7[/latex] if they sell partial cubic yards)