1、Part VII Systems of linear inequalities word problems1. Anouk is an engineer planning sound and lighting for a free concert in the park. The concert was advertised with a promise to use no more than108kilowatts(kW) of power. It was determined that the main contributors to power usage, speakers and f
2、loodlights, use1.8 kW and2.2kW, respectively. Anouk also must keep within her budget of$3,300. The rental company is charging$75for each speaker and$42for each floodlight. Which of the following combinations meets Anouks requirements?A. 40 speakers and 30 floodlightsB. 12 speakers and 54 floodlights
3、C. 26 speakers and 13 floodlightsD. 38 speakers and 22 floodlightsCORRECT ANSWER: C DIFFICULTY LEVEL: 22. In order to keep a malfunctioning satellite from falling into the earth, space agency officials decide to use a powerful rocket. At the time the rocket is attached, the satellite will be traveli
4、ng with an initial velocity, , and for every second that the rocket fires, it will add approximately 180 meters per second, to this velocity. In order to ensure safety on earth, the velocity must be increased to at least 3,800 . Also, the rocket can fire for no more than 4 seconds. For the initial v
5、elocity of the satellite, , which of the following systems of inequalities best models this situation, where t is time, in seconds, after the rocket is first fired?A. +180t3,800, t4B. +180t3,800, 180t4C. +3,800180t, t4D. +3,800180t, 180t4CORRECT ANSWER: A DIFFICULTY LEVEL: 23. Vijay needs to take a
6、taxi, which costs a flat fee of 3 dollars, plus an additional 4 dollars per mile. If Vijay has a dollars with him, which inequality shows the number of miles, m, he can afford to travel in the taxi?A. 0m4a3B. C. 4a3mD. CORRECT ANSWER : B DIFFICULTY LEVEL : 24. The change machine at an arcade gives c
7、hange in the form of 25-cent coins (quarters) and one-dollar bills. The manager of the arcade would like at least $50 worth of quarters and $100 worth of one-dollar bills in the machine at all times. Also, the manager does not allow more than $500 in the machine at any time. What is the maximum numb
8、er of quarters the manager would allow in the change machine?A. 200B. 400C. 1600D.2000CORRECT ANSWER: C DIFFICULTY LEVEL: 25. In order to bring his business to the next level, Christov wants to gain at least 2,000 followers on a popular social media platform. From his own personal account, he knows
9、that each original post gains him approximately 3 new followers and every 5 reposts gains about 1. Which of the following inequalities represents the numbers of posts, P, and reposts, R, Christov needs to reach his goal of gaining 2,000 followers?A. 3P+0.2R2,000B. 3P+5R2,000C. 1P+5R2,000D. 0.2P+5R2,
10、000CORRECT ANSWER: A DIFFICULTY LEVEL: 26. A company sells candy in jars that each have a volume of 3 cups. Each jar is filled above a certain line, guaranteeing that it has more than cups of candy. Which of the following graphs shows the possible volumes of candy, c, in cups, a customer may have, g
11、iven that they bought j jars of candy? A. B. C. D.CORRECT ANSWER: B DIFFICULTY LEVEL: 37. In a baseball game, a player must touch 4 bases to get a run. However, some players get out before reaching the base, in which case the bases dont contribute towards a run. Let b be the total number of bases a
12、player touches in one game and r be the total number of runs he gets from those bases. Which of the following graphs shows the possible number of bases a player touches, given the number of runs he gets?A. B.C. D.CORRECT ANSWER: C DIFFICULTY LEVEL: 38. Prachi needs between 240 and 260 total feet of
13、fence panels. The home improvement store has 24 short (6-foot) fence panels and 28 long (8-foot) fence panels in stock. Which of the following combinations of fence panels could she buy?A. 6 short fence panels and 26 long fence panelsB. 8 short fence panels and 23 long fence panelsC. 27 short fence
14、panels and 12 long fence panelsD. 30 short fence panels and 10 long fence panelsCORRECT ANSWER: A DIFFICULTY LEVEL: 39. Li Qiang is listening to a symphony that has 2 movements. The first movement has 3 beats per measure and the second movement has 4 beats per measure. The symphony has 446 measures.
15、 In an attempt to count the beats, Li Qiang counts at least x of the beats in the first movement and exactly b beats in the second movement. Let x be the number of beats in the first movement and b be the number of beats in the second movement. Which of the following inequalities must be true?A.B.C.
16、D.CORRECT ANSWER: A DIFFICULTY LEVEL: 310. Priyankas car gets a maximum of 35 miles per gallon. According to a particular convention, the“wear”on a vehicle is at least times the total number of miles driven plus the total number of gallons used. For Priyankas car, let m be the total number of miles
17、driven, let g be the total number of gallons used, and let w be the “wear”. Which of the following systems of inequalities correctly represents these relationships?A.B.C.D.CORRECT ANSWER: A DIFFICULTY LEVEL: 311.In night vision goggles, light rays cause electrons to be projected from a metal surface
18、. The above equation relates the kinetic energy in electron volts (eV), K, of emitted electrons to the frequency in hertz, , of incident light rays and the work function, , in eV, of the metallic surface.In a particular set of night vision goggles, the electrons emitted must have a kinetic energy of
19、 at least 2.46 eV. If the frequency of incoming light rays is less than hertz , which of the following systems of inequalities best models the relationship between the work function, , and the light source frequency, ?A.B.C.D.CORRECT ANSWER: B DIFFICULTY LEVEL: 212. Paper Scraper, Inc, a mobile pape
20、r shredding and recycling company, receives $0.39 for each pound of paper they shred, but it costs them approximately $1.38 per mile to operate their truck. Any job that requires less than 200 miles of travel, and also nets at least $500 profit, qualifies for free delivery. Of the following, which c
21、ombination of size in pounds and distance in miles would qualify for free delivery?A. Paul has 1,100 pounds of paper that requires 3 miles of travel.B. Li Min has 1,500 pounds of paper that requires 107 miles of travel.C. Amira has 1,800 pounds of paper that requires 94 miles of travel.D. Jarles has
22、 3,500 pounds of paper that requires 225 miles of travel.CORRECT ANSWER: C DIFFICULTY LEVEL: 213. When Suraj goes to Roycefield golf course, he loses 20% of the (golf) balls he uses. When he goes to Hunterdon golf course, he loses 30% of the balls he uses. It costs Suraj $1.20 to buy a ball. This we
23、ekend, Suraj is planning to use 25 balls at Roycefield and 30 balls at Hunterdon. If he only has $20 to spend on balls, how many balls can he buy in order to guarantee that he will be able to replace the balls he loses this weekend?A. 5B. 10C. 15D. 20CORRECT ANSWER: C DIFFICULTY LEVEL: 214. A techno
24、logy store sells tablets and computers. In January they sell over 300 items, and more of those sales are tablets than computers. In February they sell exactly 100 tablets and 20 computers. The graph at left shows two equations related to this problem, where t is the total tablet sales (in January an
25、d February combined), and c is the total computer sales. Which of the following combinations could be the technology stores total sales?A. 240 tablets and 100 computersB. 360 tablets and 180 computersC. 240 tablets and 260 computersD. 120 tablets and 180 computersCORRECT ANSWER: B DIFFICULTY LEVEL:
26、215. Elena is designing a paint can with thickness t millimeters and height h centimeters. She calculates that the thickness of the can in milimeters must be at least 0.1 times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used, (0
27、.2+t+0.5h) cents, must be at most 12.2 cents. Which of the following systems of inequalities best models the relationship between height and thickness described above?A.B.C.D.CORRECT ANSWER: A DIFFICULTY LEVEL: 216. Anna is considering three insurance options for her business, shown in the table bel
28、ow.She wants the total cost, c+d, to be at most $2,000. She also wants the benefit, which is 9090 percent of (10cd), to be at least $12,400. Which of the following option selections would fit Annas plan?A. Options 11 and 22 workB. Only option 22 worksC. Only option 33 worksD. None of the aboveCORREC
29、T ANSWER: A DIFFICULTY LEVEL: 217. Aaron is purchasing party hats and fake mustaches for an end of the school year party. He can spend at most $30. Fake mustaches cost $3 each, and party hats cost $2 each. If he must purchase a combination of at least 15 mustaches and party hats, which of the follow
30、ing systems of inequalities best models the relationship between the number of mustaches, m, and party hats, p, described above?A.B.C.D.CORRECT ANSWER: A DIFFICULTY LEVEL: 218. A company manufactures cellular phones and laptop computers. The companys daily production of cellular phones, c, must be m
31、ore than 500,000, and its daily production of laptop computers, l, must be more than 300,000. If the maximum capacity of the companys manufacturing center is no more than 950,000 total cellular phones and laptop computers, which of the following systems of inequalities best models the situation desc
32、ribed above?A.B.C.D.CORRECT ANSWER: D DIFFICULTY LEVEL: 219. Tony is raising funds for his school soccer team by selling boxes of candy and t-shirts. His goal is to make more than $300 dollars overall. Each box of candy that Tony sells earns him $15, and each t-shirt sold earns him $20. If Tony want
33、s to sell at least as many t-shirts as boxes of candy, then which of the following systems of inequalities best models the relationship between the number of boxes of candy, c, and t-shirts, t, described above?A.B.C.D.CORRECT ANSWER: C DIFFICULTY LEVEL: 220. Arturo goes to his neighborhood store to
34、purchase almonds and walnuts for an old family recipe. One pound of almonds costs $2, and one pound of walnuts costs $4. Arturo can spend at most $18 on almonds and walnuts. The graph at left, in the wa-plane, relates the number of pounds, w, of walnuts to the number of pounds, a, of almonds which A
35、rturo can purchase and have enough for his recipe. Which of the following amounts of walnuts and almonds can he purchase?A. 2 pounds of walnuts and 11 pound of almondsB. 33 pounds of walnuts and 77 pounds of almondsC. 44 pounds of walnuts and 22 pound of almondsD. 22 pounds of walnuts and 44 pounds
36、of almondsCORRECT ANSWER: D DIFFICULTY LEVEL: 221.In a standard economic supply and demand graph, consumer surplus is defined as the area greater than or equal to the equilibrium price of a good and less than or equal to the demand line. The system of linear inequalities written and graphed at left,
37、 where p represents price and q represents the quantity of units that consumers will demand, shows the consumer surplus area for a tablet computer that recently entered the U.S. marketplace. What is the maximum quantity of the tablet that consumers will demand and still have it remain in the consume
38、r surplus area of the graph?A. 200B. 800C. 2800D. 3000CORRECT ANSWER: D DIFFICULTY LEVEL: 222. Julia mows lawns in the summer for $15 per lawn. It costs Julia between $2 and $4 to mow 1 lawn. If l represents the number of lawns Julia mows, which graph correctly shades the possible values of Julias n
39、et earnings, d, in dollars?A. B.C. D.CORRECT ANSWER: B DIFFICULTY LEVEL: 323. The florist needs at least gallons of nutrient-rich water for each bushel of flowers he buys. With $120 to spend this week, the florist purchases f bushels of flowers at $1.19 per bushel and w gallons of nutrient-rich wate
40、r at $0.50 per gallon. The equations related to these two constraints are graphed at left. How many bushels of flowers and gallons of nutrient-rich water could he buy?A. 120 bushels of flowers and 20 gallons of nutrient-rich waterB. 100 bushels of flowers and 80 gallons of nutrient-rich waterC. 60 b
41、ushels of flowers and 40 gallons of nutrient-rich waterD. 80 bushels of flowers and 10 gallons of nutrient-rich waterCORRECT ANSWER: C DIFFICULTY LEVEL: 324. Ceclia has 2 jobs. The first job pays $8.20 per hour and the second job pays $14.60 per hour. Each week, Ceclia can work no more than 40 hours
42、, but she needs to make at least $440. In one week, Ceclia works a hours at the first job and b hours at the second job. Which graph represents the number of hours that Ceclia can work at each of her two jobs to satisfy these conditions?A. B. C. D. CORRECT ANSWER: B DIFFICULTY LEVEL: 325. A landscap
43、ing company sells bags that hold up to 2.25 cubic feet ()of mulch. The company guarantees that there is at least 2of mulch inside each bag. The graph at left shows two equations related to this problem, where b is the number of bags of mulch and v is the cubic feet of mulch. Which of the following p
44、urchases could have come from this company?A. 12 bags of mulch containing of mulchB. 14 bags of mulch containing of mulchC. 16 bags of mulch containing of mulchD. 18 bags of mulch containing of mulchCORRECT ANSWER: C DIFFICULTY LEVEL: 326. A barge must carry steel pieces for a construction project s
45、uch that the total weight of the steel pieces is under 1,500,000 kilograms (kg). Each steel piece is either a beam, which weighs 363kg, or a connector plate, which weighs 6kg. There must be at least 2 connector plates for each beam. If b is the number of beams and c is the number of connector plates
46、, which of the following systems of inequalities must be true?A.B.C.D.CORRECT ANSWER: B DIFFICULTY LEVEL: 327. A car dealership can have up to 90 cars on its lot. According to dealership predictions, when the average number of cars on the lot is 60, then at most 480 cars are sold per year. Whenever the average number of cars on the lot increases by 1, the dealership sells up to 2 more cars per year. Which of the following graphs represents the predicted car sales per year, S, based on the average number of cars o