18.1: Problem Solving
1. \(18 / 230=0.07826=\) about \(7.8 \%\)
3. \(€ 250(0.23)=€ 57.50\) in VAT
5. \(\$ 15000(5.57)=\$ 83,550\)
7. absolute increase: \(1050 .\) Relative: \(1050 / 3250=0.323=32.3 \%\) increase
9.
- \(2200-2200(0.15)=2200(0.85)=1 \$ 1870\)
- Yes, their goal was to decrease by at least 15%. They exceeded their goal.
11. Dropping by \(6 \%\) is the same as keeping \(94 \%\). \(a(0.94)=300 . a=319.15 .\) Attendance was about 319 before the drop.
13.
a) Kaplan’s enrollment was 64.3% larger than Walden’s. 30510
b) Walden’s enrollment was 39.1% smaller than Kaplan’s.
c) Walden’s enrollment was 60.9% of Kaplan’s.
15. If the original price was \(\$ 100,\) the basic clearance price would be \(\$ 100-\$ 100(0.60)=\$ 40 .\) The additional markdown would bring it to \(\$ 40-\$ 40(0.30)=\$ 28 .\) This is \(28 \%\) 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 $9.33 per $1000, which is 0.933% tax rate. If the original rate was 0.833% (0.1 percentage point lower), then this would indeed be a 12% relative increase.
23. \(20 \%\) of \(30 \%\) is \(30 \%(0.20)=6 \%,\) a 6 percentage point decrease.
25. Probably not, unless the final is worth 50% of the overall class grade. If the final was worth 25% of the overall grade, then a 100% would only raise her average to 77.5%
27. \(\$ 4 / 10\) pounds \(=\$ 0.40\) per pound (or 10 pounds/\$4 \(=2.5\) pounds per dollar)
29. \(x=15\)
31. 2.5 cups
33. 74 turbines
35. 96 inches
37. $6000
39. 55.6 meters
43. The population density of the US is 84 people per square mile. The density of India is about 933 people per square mile. The density of India is about 11 times greater than that of the U.S.
49. The oil in the spill could produce 93.1 million gallons of gasoline. Each car uses about 600 gallons a year. That would fuel 155,167 cars for a year.
53. An answer around 100-300 gallons would be reasonable
57. 156 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. 750 miles/hr is about 0.21 miles/sec. If the sound takes 4 seconds to reach you, the lightning is about 0.84 miles away. In general, the lightning will be \(0.21 n\) miles away, which is often approximated by dividing the number of seconds by 5
61. About 8.2 minutes
63. Four cubic yards (or 3.7 if they sell partial cubic yards)