1. Out of [latex]230[/latex] racers who started the marathon, [latex]212[/latex] completed the race, [latex]14[/latex] gave up, and [latex]4[/latex] were disqualified. What percentage did not complete the marathon?
2. Patrick left an [latex]$8[/latex] tip on a [latex]$50[/latex] restaurant bill. What percent tip is that?
3. Ireland has a [latex]23\%[/latex] VAT (value-added tax, similar to a sales tax). How much will the VAT be on a purchase of a €250 item?
   Employees in [latex]2012[/latex] paid [latex]4.2\%[/latex] of their gross wages towards social security (FICA tax), while employers paid another [latex]6.2\%[/latex]. How much will someone earning [latex]$45,000[/latex] a year pay towards social security out of their gross wages?
4. A project on Kickstarter.com was aiming to raise [latex]$15,000[/latex] for a precision coffee press. They ended up with [latex]714[/latex] supporters, raising [latex]557\%[/latex] of their goal. How much did they raise?
   Another project on Kickstarter for an iPad stylus raised [latex]1,253\%[/latex] of their goal, raising a total of [latex]$313,490[/latex] from [latex]7,511[/latex] supporters. What was their original goal?
5. The population of a town increased from [latex]3,250[/latex] in [latex]2008[/latex] to [latex]4,300[/latex] in [latex]2010[/latex]. Find the absolute and relative (percent) increase.
6. The number of CDs sold in [latex]2010[/latex] was [latex]114[/latex] million, down from [latex]147[/latex] million the previous year^[1]. Find the absolute and relative (percent) decrease.
7. A company wants to decrease their energy use by [latex]15\%[/latex].
   • If their electric bill is currently [latex]$2,200[/latex] a month, what will their bill be if they’re successful?
   • If their next bill is [latex]$1,700[/latex] a month, were they successful? Why or why not?
8. A store is hoping an advertising campaign will increase their number of customers by [latex]30\%[/latex]. They currently have about [latex]80[/latex] customers a day.
   • How many customers will they have if their campaign is successful?
   • If they increase to [latex]120[/latex] customers a day, were they successful? Why or why not?
9. An article reports “attendance dropped [latex]6\%[/latex] this year, to [latex]300[/latex].” What was the attendance before the drop?
10. An article reports “sales have grown by [latex]30\%[/latex] this year, to [latex]$200[/latex] million.” What were sales before the growth?
11. Walden University had [latex]47,456[/latex] students in [latex]2010[/latex], while Kaplan University had [latex]77,966[/latex] students. Complete the following statements:
    • Kaplan’s enrollment was ___[latex]\%[/latex] larger than Walden’s.
    • Walden’s enrollment was ___[latex]\%[/latex] smaller than Kaplan’s.
    • Walden’s enrollment was ___[latex]\%[/latex] of Kaplan’s.
12. In the [latex]2012[/latex] Olympics, Usain Bolt ran the [latex]100[/latex]m dash in [latex]9.63[/latex] seconds. Jim Hines won the [latex]1968[/latex] Olympic gold with a time of [latex]9.95[/latex] seconds.
    • Bolt’s time was ___[latex]\%[/latex] faster than Hines’.
    • Hines’ time was ___[latex]\%[/latex] slower than Bolt’s.
    • Hines’ time was ___[latex]\%[/latex] of Bolt’s.
13. A store has clearance items that have been marked down by [latex]60\%[/latex]. They are having a sale, advertising an additional [latex]30\%[/latex] off clearance items. What percent of the original price do you end up paying?
14. Which is better: having a stock that goes up [latex]30\%[/latex] on Monday than drops [latex]30\%[/latex] on Tuesday, or a stock that drops [latex]30\%[/latex] on Monday and goes up [latex]30\%[/latex] on Tuesday? In each case, what is the net percent gain or loss?
15. Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
    • “[latex]16.3\%[/latex] of Americans are without health insurance.”^[2]
    • “only [latex]55.9\%[/latex] of adults receive employer provided health insurance.”^[3]
16. Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
    • “We mark up the wholesale price by [latex]33\%[/latex] to come up with the retail price.”
    • “The store has a [latex]25\%[/latex] profit margin.”
17. Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
    • “Every year since [latex]1950[/latex], the number of American children gunned down has doubled.”
    • “The number of child gunshot deaths has doubled from [latex]1950[/latex] to [latex]1994[/latex].”
18. Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?^[4]
    • “[latex]75[/latex] percent of the federal health care law’s taxes would be paid by those earning less than [latex]$120,000[/latex] a year.”
    • “[latex]76[/latex] percent of those who would pay the penalty [health care law’s taxes] for not having insurance in [latex]2016[/latex] would earn under [latex]$120,000[/latex].”
19. Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
    • “The school levy is only a [latex]0.1\%[/latex] increase of the property tax rate.”
    • “This new levy is a [latex]12\%[/latex] tax hike, raising our total rate to [latex]$9.33[/latex] per [latex]$1000[/latex] of value.”
20. Are the values compared in this statement comparable or not comparable? “Guns have murdered more Americans here at home in recent years than have died on the battlefields of Iraq and Afghanistan. In support of the two wars, more than [latex]6,500[/latex]American soldiers have lost their lives. During the same period, however, guns have been used to murder about [latex]100,000[/latex] people on American soil.”^[5]
21. A high school currently has a [latex]30\%[/latex] dropout rate. They’ve been tasked to decrease that rate by [latex]20\%[/latex]. Find the equivalent percentage point drop.
22. A politician’s support grew from [latex]42\%[/latex] by [latex]3[/latex] percentage points to [latex]45\%[/latex]. What percent (relative) change is this?
23. Marcy has a [latex]70\%[/latex] average in her class going into the final exam. She says “I need to get a [latex]100\%[/latex] on this final so I can raise my score to [latex]85\%[/latex].” Is she correct?
24. Suppose you have one quart of water/juice mix that is [latex]50\%[/latex] juice, and you add [latex]2[/latex] quarts of juice. What percent juice is the final mix?
25. Find a unit rate:   You bought [latex]10[/latex] pounds of potatoes for [latex]$4[/latex].
26. Find a unit rate: Joel ran [latex]1500[/latex] meters in [latex]4[/latex] minutes, [latex]45[/latex] seconds.
27. A crepe recipe calls for [latex]2[/latex] eggs, [latex]1[/latex] cup of flour, and [latex]1[/latex] cup of milk. How much flour would you need if you use [latex]5[/latex] eggs?
28. An [latex]8[/latex]ft length of [latex]4[/latex] inch wide crown molding costs [latex]$14[/latex]. How much will it cost to buy [latex]40[/latex]ft of crown molding?
29. Four [latex]3[/latex]-megawatt wind turbines can supply enough electricity to power [latex]3000[/latex] homes. How many turbines would be required to power [latex]55,000[/latex] homes?
30. A highway had a landslide, where [latex]3,000[/latex] cubic yards of material fell on the road, requiring [latex]200[/latex] dump truck loads to clear. On another highway, a slide left [latex]40,000[/latex] cubic yards on the road. How many dump truck loads would be needed to clear this slide?
31. Convert [latex]8[/latex] feet to inches.
32. Convert [latex]6[/latex] kilograms to grams.
33. A wire costs [latex]$2[/latex] per meter. How much will [latex]3[/latex] kilometers of wire cost?
34. Sugar contains [latex]15[/latex] calories per teaspoon. How many calories are in [latex]1[/latex] cup of sugar?
35. A car is driving at [latex]100[/latex] kilometers per hour. How far does it travel in [latex]2[/latex] seconds?
36. A chain weighs [latex]10[/latex] pounds per foot. How many ounces will [latex]4[/latex] inches weigh?
37. The table below gives data on three movies. Gross earnings is the amount of money the movie brings in. Compare the net earnings (money made after expenses) for the three movies.^[6]

     

    Movie	Release Date	Budget	Gross earnings
    Saw	[latex]10/29/2004[/latex]	[latex]$1,200,000[/latex]	[latex]$103,096,345[/latex]
    Titanic	[latex]12/19/1997[/latex]	[latex]$200,000,000[/latex]	[latex]$1,842,879,955[/latex]
    Jurassic Park	[latex]6/11/1993[/latex]	[latex]$63,000,000[/latex]	[latex]$923,863,984[/latex]

     

38. For the movies in the previous problem, which provided the best return on investment?
39. The population of the U.S. is about [latex]309,975,000[/latex], covering a land area of [latex]3,717,000[/latex] square miles. The population of India is about [latex]1,184,639,000[/latex], covering a land area of [latex]1,269,000[/latex] square miles. Compare the population densities of the two countries.
40. The GDP (Gross Domestic Product) of China was [latex]$5,739[/latex] billion in 2010, and the GDP of Sweden was [latex]$435[/latex] billion. The population of China is about [latex]1,347[/latex] million, while the population of Sweden is about [latex]9.5[/latex] million. Compare the GDP per capita of the two countries.
41. In June 2012, Twitter was reporting [latex]400[/latex] million tweets per day. Each tweet can consist of up to [latex]140[/latex] characters (letter, numbers, etc.). Create a comparison to help understand the amount of tweets in a year by imagining each character was a drop of water and comparing to filling something up.
42. The photo sharing site Flickr had [latex]2.7[/latex] billion photos in June [latex]2012[/latex]. Create a comparison to understand this number by assuming each picture is about [latex]2[/latex] megabytes in size, and comparing to the data stored on other media like DVDs, iPods, or flash drives.
43. Your chocolate milk mix says to use [latex]4[/latex] scoops of mix for [latex]2[/latex] cups of milk. After pouring in the milk, you start adding the mix, but get distracted and accidentally put in [latex]5[/latex] scoops of mix. How can you adjust the mix if:
    • There is still room in the cup?
    • The cup is already full?
44. A recipe for sabayon calls for [latex]2[/latex] egg yolks, [latex]3[/latex] tablespoons of sugar, and [latex]¼[/latex] cup of white wine. After cracking the eggs, you start measuring the sugar, but accidentally put in [latex]4[/latex] tablespoons of sugar. How can you compensate?
45. The Deepwater Horizon oil spill resulted in [latex]4.9[/latex] million barrels of oil spilling into the Gulf of Mexico. Each barrel of oil can be processed into about [latex]19[/latex] gallons of gasoline. How many cars could this have fueled for a year? Assume an average car gets [latex]20[/latex] miles to the gallon, and drives about [latex]12,000[/latex] miles in a year.
46. The store is selling lemons at [latex]2[/latex] for [latex]$1[/latex]. Each yields about [latex]2[/latex] tablespoons of juice. How much will it cost to buy enough lemons to make a [latex]9[/latex]-inch lemon pie requiring [latex]½[/latex] cup of lemon juice?
47. A piece of paper can be made into a cylinder in two ways: by joining the short sides together, or by joining the long sides together^[7]. Which cylinder would hold more? How much more?
48. Which of these glasses contains more liquid? How much more?

In the next 4 questions, estimate the values by making reasonable approximations for unknown values, or by doing some research to find reasonable values.

51. Estimate how many gallons of water you drink in a year.
52. Estimate how many times you blink in a day.
53. How much does the water in a [latex]6[/latex]-person hot tub weigh?
54. How many gallons of paint would be needed to paint a two-story house [latex]40[/latex] ft long and [latex]30[/latex] ft wide?
55. During the landing of the Mars Science Laboratory Curiosity, it was reported that the signal from the rover would take [latex]14[/latex] minutes to reach earth. Radio signals travel at the speed of light, about [latex]186,000[/latex] miles per second. How far was Mars from Earth when Curiosity landed?
56. It is estimated that a driver takes, on average, [latex]1.5[/latex] seconds from seeing an obstacle to reacting by applying the brake or swerving. How far will a car traveling at [latex]60[/latex] miles per hour travel (in feet) before the driver reacts to an obstacle?
57. The flash of lightning travels at the speed of light, which is about [latex]186,000[/latex] miles per second. The sound of lightning (thunder) travels at the speed of sound, which is about [latex]750[/latex] miles per hour.
    • If you see a flash of lightning, then hear the thunder [latex]4[/latex] seconds later, how far away is the lightning?
    • Now let’s generalize that result. Suppose it takes n seconds to hear the thunder after a flash of lightning. How far away is the lightning, in terms of n?
58. Sound travels about [latex]750[/latex] miles per hour. If you stand in a parking lot near a building and sound a horn, you will hear an echo.
    • Suppose it takes about [latex]½[/latex] a second to hear the echo. How far away is the building^[8]?
    • Now let’s generalize that result. Suppose it takes n seconds to hear the echo. How far away is the building, in terms of n?
59. It takes an air pump [latex]5[/latex] minutes to fill a twin sized air mattress ([latex]39[/latex] by [latex]8.75[/latex] by [latex]75[/latex] inches). How long will it take to fill a queen sized mattress ([latex]60[/latex] by [latex]8.75[/latex] by [latex]80[/latex] inches)?
60. It takes your garden hose [latex]20[/latex] seconds to fill your [latex]2[/latex]-gallon watering can. How long will it take to fill
    • An inflatable pool measuring [latex]3[/latex] feet wide, [latex]8[/latex] feet long, and [latex]1[/latex] foot deep.^[9]
    • A circular inflatable pool [latex]13[/latex] feet in diameter and [latex]3[/latex] feet deep.^[10]
61. You want to put a [latex]2[/latex]” thick layer of topsoil for a new [latex]20[/latex]‘x[latex]30[/latex]‘ garden.  The dirt store sells by the cubic yards. How many cubic yards will you need to order?
62. A box of Jell-O costs [latex]$0.50[/latex], and makes [latex]2[/latex] cups. How much would it cost to fill a swimming pool [latex]4[/latex] feet deep, [latex]8[/latex] feet wide, and [latex]12[/latex] feet long with Jell-O? (1 cubic foot is about [latex]7.5[/latex] gallons)
63. You read online that a [latex]15[/latex] ft by [latex]20[/latex] ft brick patio would cost about [latex]$2,275[/latex] to have professionally installed. Estimate the cost of having a [latex]18[/latex] by [latex]22[/latex] ft brick patio installed.
64. I was at the store, and saw two sizes of avocados being sold. The regular size sold for [latex]$0.88[/latex] each, while the jumbo ones sold for [latex]$1.68[/latex] each. Which is the better deal?
65. The grocery store has bulk pecans on sale, which is great since you’re planning on making [latex]10[/latex] pecan pies for a wedding. Your recipe calls for [latex]1¾[/latex] cups pecans per pie. However, in the bulk section there’s only a scale available, not a measuring cup. You run over to the baking aisle and find a bag of pecans, and look at the nutrition label to gather some info. How many pounds of pecans should you buy?
66. Soda is often sold in [latex]20[/latex] ounce bottles. The nutrition label for one of these bottles is shown to the right. A packet of sugar (the kind they have at restaurants for your coffee or tea) typically contain [latex]4[/latex] grams of sugar in the U.S. Drinking a [latex]20[/latex] oz soda is equivalent to eating how many packets of sugar?^[11]

For the next set of questions, first identify the information you need to answer the question, and then scroll down to the bottom of the page to find that information. The details may be imprecise; answer the question the best you can with the provided information. Be sure to justify your decision.

67. You’re planning on making [latex]6[/latex] meatloafs for a party. You go to the store to buy breadcrumbs, and see they are sold by the canister. How many canisters do you need to buy?
68. Your friend wants to cover her car in bottle caps, like in this picture. How many bottle caps will she need?
    
69. You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for [latex]$2.99[/latex] a pound, which is cheaper than your usual neighborhood store, which sells it for [latex]$3.79[/latex] a pound.   Is it worth the extra drive?
70. I have an old gas furnace, and am considering replacing it with a new, high efficiency model. Is upgrading worth it?
71. Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money?
72. Marcus is considering going car-free to save money and be more environmentally friendly. Is this financially a good decision?

For the next set of problems, research or make educated estimates for any unknown quantities needed to answer the question.

73. You want to travel from Tacoma, WA to Chico, CA for a wedding. Compare the costs and time involved with driving, flying, and taking a train. Assume that if you fly or take the train you’ll need to rent a car while you’re there. Which option is best?
74. You want to paint the walls of a [latex]6[/latex]ft by [latex]9[/latex]ft storage room that has one door and one window. You want to put on two coats of paint. How many gallons and/or quarts of paint should you buy to paint the room as cheaply as possible?
75. A restaurant in New York tiled their floor with pennies^[12]. Just for the materials, is this more expensive than using a more traditional material like ceramic tiles? If each penny has to be laid by hand, estimate how long it would take to lay the pennies for a [latex]12[/latex]ft by [latex]10[/latex]ft room. Considering material and labor costs, are pennies a cost-effective replacement for ceramic tiles?
76. You are considering taking up part of your back yard and turning it into a vegetable garden, to grow broccoli, tomatoes, and zucchini. Will doing so save you money, or cost you more than buying vegetables from the store?
77. Barry is trying to decide whether to keep his [latex]1993[/latex] Honda Civic with [latex]140,000[/latex] miles, or trade it in for a used [latex]2008[/latex] Honda Civic. Consider gas, maintenance, and insurance costs in helping him make a decision.
78. Some people claim it costs more to eat a vegetarian diet, while some claim it costs less. Examine your own grocery habits, and compare your current costs to the costs of switching your diet (from omnivore to vegetarian or vice versa as appropriate). Which diet is more cost effective based on your eating habits?

 

Information for questions 67-71.

 

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