7Systems of linear inequalities word probWord文档格式.docx
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foreachspeakerand
$42
foreachfloodlight.WhichofthefollowingcombinationsmeetsAnouk'
srequirements?
A.40speakersand30floodlights
B.12speakersand54floodlights
C.26speakersand13floodlights
D.38speakersand22floodlights
CORRECTANSWER:
CDIFFICULTYLEVEL:
2
2.Inordertokeepamalfunctioningsatellitefromfallingintotheearth,spaceagencyofficialsdecidetouseapowerfulrocket.Atthetimetherocketisattached,thesatellitewillbetravelingwithaninitialvelocity,
andforeverysecondthattherocketfires,itwilladdapproximately180meterspersecond,
tothisvelocity.Inordertoensuresafetyonearth,thevelocitymustbeincreasedtoatleast3,800
.Also,therocketcanfirefornomorethan4seconds.Fortheinitialvelocityofthesatellite,
whichofthefollowingsystemsofinequalitiesbestmodelsthissituation,wheretistime,inseconds,aftertherocketisfirstfired?
A.
+180t≥3,800,t≤4
B.
+180t≥3,800,180t≤4
C.
+3,800≤180t,t≤4
D.
+3,800≤180t,180t≤4
ADIFFICULTYLEVEL:
3.Vijayneedstotakeataxi,whichcostsaflatfeeof3dollars,plusanadditional4dollarspermile.IfVijayhasadollarswithhim,whichinequalityshowsthenumberofmiles,m,hecanaffordtotravelinthetaxi?
A.0≤m≤4a−3
C.4a−3≤m
CORRECTANSWER:
BDIFFICULTYLEVEL:
4.Thechangemachineatanarcadegiveschangeintheformof25-centcoins(quarters)andone-dollarbills.Themanagerofthearcadewouldlikeatleast$50worthofquartersand$100worthofone-dollarbillsinthemachineatalltimes.Also,themanagerdoesnotallowmorethan$500inthemachineatanytime.Whatisthemaximumnumberofquartersthemanagerwouldallowinthechangemachine?
A.200
B.400
C.1600
D.2000
5.Inordertobringhisbusinesstothenextlevel,Christovwantstogainatleast2,000followersonapopularsocialmediaplatform.Fromhisownpersonalaccount,heknowsthateachoriginalpostgainshimapproximately3newfollowersandevery5repostsgainsabout1.Whichofthefollowinginequalitiesrepresentsthenumbersofposts,P,andreposts,R,Christovneedstoreachhisgoalofgaining2,000followers?
A.3P+0.2R≥2,000
B.3P+5R≤2,000
C.1P+5R≥2,000
D.0.2P+5R≤2,000
6.Acompanysellscandyinjarsthateachhaveavolumeof3cups.Eachjarisfilledaboveacertainline,guaranteeingthatithasmorethan
cupsofcandy.Whichofthefollowinggraphsshowsthepossiblevolumesofcandy,c,incups,acustomermayhave,giventhattheyboughtjjarsofcandy?
A.B.
C.D.
BDIFFICULTYLEVEL:
3
7.Inabaseballgame,aplayermusttouch4basestogetarun.However,someplayersget"
out"
beforereachingthe
base,inwhichcasethebasesdon'
tcontributetowardsarun.Letbbethetotalnumberofbasesaplayertouchesinonegameandrbethetotalnumberofrunshegetsfromthosebases.Whichofthefollowinggraphsshowsthepossiblenumberofbasesaplayertouches,giventhenumberofrunshegets?
C.D.
8.Prachineedsbetween240and260totalfeetoffencepanels.Thehomeimprovementstorehas24short(6-foot)fencepanelsand28long(8-foot)fencepanelsinstock.Whichofthefollowingcombinationsoffencepanelscouldshebuy?
A.6shortfencepanelsand26longfencepanels
B.8shortfencepanelsand23longfencepanels
C.27shortfencepanelsand12longfencepanels
D.30shortfencepanelsand10longfencepanels
9.LiQiangislisteningtoasymphonythathas2movements.Thefirstmovementhas3beatspermeasureandthesecondmovementhas4beatspermeasure.Thesymphonyhas446measures.Inanattempttocountthebeats,LiQiangcountsatleastxofthebeatsinthefirstmovementandexactlybbeatsinthesecondmovement.Letxbethenumberofbeatsinthefirstmovementandbbethenumberofbeatsinthesecondmovement.Whichofthefollowinginequalitiesmustbetrue?
10.Priyanka'
scargetsamaximumof35milespergallon.Accordingtoaparticularconvention,the“wear”onavehicleisatleast
timesthetotalnumberofmilesdrivenplusthetotalnumberofgallonsused.ForPriyanka'
scar,letmbethetotalnumberofmilesdriven,letgbethetotalnumberofgallonsused,andletwbethe“wear”.Whichofthefollowingsystemsofinequalitiescorrectlyrepresentstheserelationships?
11.
Innightvisiongoggles,lightrayscauseelectronstobeprojectedfromametalsurface.Theaboveequationrelatesthekineticenergyinelectronvolts(eV),K,ofemittedelectronstothefrequencyinhertz,
ofincidentlightraysandtheworkfunction,
ineV,ofthemetallicsurface.
Inaparticularsetofnightvisiongoggles,theelectronsemittedmusthaveakineticenergyofatleast2.46eV.Ifthefrequencyofincominglightraysislessthan
hertz,whichofthefollowingsystemsofinequalitiesbestmodelstherelationshipbetweentheworkfunction,
andthelightsourcefrequency,
?
12.PaperScraper,Inc,amobilepapershreddingandrecyclingcompany,receives$0.39foreachpoundofpapertheyshred,butitcoststhemapproximately$1.38permiletooperatetheirtruck.Anyjobthatrequireslessthan200milesoftravel,andalsonetsatleast$500profit,qualifiesforfreedelivery.Ofthefollowing,whichcombinationofsizeinpoundsanddistanceinmileswouldqualifyforfreedelivery?
A.Paulhas1,100poundsofpaperthatrequires3milesoftravel.
B.LiMinhas1,500poundsofpaperthatrequires107milesoftravel.
C.Amirahas1,800poundsofpaperthatrequires94milesoftravel.
D.Jarleshas3,500poundsofpaperthatrequires225milesoftravel.
13.WhenSurajgoestoRoycefieldgolfcourse,heloses20%ofthe(golf)ballsheuses.WhenhegoestoHunterdongolfcourse,heloses30%oftheballsheuses.ItcostsSuraj$1.20tobuyaball.Thisweekend,Surajisplanningtouse25ballsatRoycefieldand30ballsatHunterdon.Ifheonlyhas$20tospendonballs,howmanyballscanhebuyinordertoguaranteethathewillbeabletoreplacetheballshelosesthisweekend?
A.5
B.10
C.15
D.20
14.Atechnologystoresellstabletsandcomputers.InJanuarytheysellover300items,andmoreofthosesalesaretabletsthancomputers.InFebruarytheysellexactly100tabletsand20computers.Thegraphatleftshowstwoequationsrelatedtothisproblem,wheretisthetotaltabletsales(inJanuaryandFebruarycombined),andcisthetotalcomputersales.Whichofthefollowingcombinationscouldbethetechnologystore'
stotalsales?
A.240tabletsand100computers
B.360tabletsand180computers
C.240tabletsand260computers
D.120tabletsand180computers
15.Elenaisdesigningapaintcanwiththicknesstmillimetersandheighthcentimeters.Shecalculatesthatthethicknessofthecaninmilimetersmustbeatleast0.1timestheheightofthecanincentimetersinordertowithstandpressure.Duetocostconstraints,thecostofmaterialused,(0.2+t+0.5h)cents,mustbeatmost12.2cents.Whichofthefollowingsystemsofinequalitiesbestmodelstherelationshipbetweenheightandthicknessdescribedabove?
16.Annaisconsideringthreeinsuranceoptionsforherbusiness,showninthetablebelow.
Shewantsthetotalcost,c+d,tobeatmost$2,000.Shealsowantsthebenefit,whichis9090percentof(10c−d),tobeatleast$12,400.WhichofthefollowingoptionselectionswouldfitAnna'
splan?
A.Options11and22work
B.Onlyoption22works
C.Onlyoption33works
D.Noneoftheabove
17.Aaronispurchasingpartyhatsandfakemustachesforanendoftheschoolyearparty.Hecanspendatmost$30.Fakemustachescost$3each,andpartyhatscost$2each.Ifhemustpurchaseacombinationofatleast15mustachesandpartyhats,whichofthefollowingsystemsofinequalitiesbestmodelstherelationshipbetweenthenumberofmustaches,m,andpartyhats,p,describedabove?
18.Acompanymanufacturescellularphonesandlaptopcomputers.Thecompany'
sdailyproductionofcellularphones,c,mustbemorethan500,000,anditsdailyproductionoflaptopcomputers,l,mustbemorethan300,000.Ifthemaximumcapacityofthecompany'
smanufacturingcenterisnomorethan950,000totalcellularphonesandlaptopcomputers,whichofthefollowingsystemsofinequalitiesbestmodelsthesituationdescribedabove?
DDIFFICULTYLEVEL:
19.Tonyisraisingfundsforhisschoolsoccerteambysellingboxesofcandyandt-shirts.Hisgoalistomakemorethan$300dollarsoverall.EachboxofcandythatTonysellsearnshim$15,andeacht-shirtsoldearnshim$20.IfTonywantstosell