7Systems of linear inequalities word prob.docx

7Systems of linear inequalities word prob.docx

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7Systemsoflinearinequalitieswordprob

PartVIISystemsoflinearinequalitieswordproblems

1.Anoukisanengineerplanningsoundandlightingforafreeconcertinthepark.Theconcertwasadvertisedwithapromisetousenomorethan 108 kilowatts （kW）ofpower.Itwasdeterminedthatthemaincontributorstopowerusage,speakersandfloodlights,use 1.8kWand 2.2 kW,respectively.Anoukalsomustkeepwithinherbudgetof $3,300.Therentalcompanyischarging $75 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

CORRECTANSWER:

ADIFFICULTYLEVEL:

2

3.Vijayneedstotakeataxi,whichcostsaflatfeeof3dollars,plusanadditional4dollarspermile.IfVijayhasadollarswithhim,whichinequalityshowsthenumberofmiles,m,hecanaffordtotravelinthetaxi?

A.0≤m≤4a−3

B.

C.4a−3≤m

D.

CORRECTANSWER:

BDIFFICULTYLEVEL:

2

4.Thechangemachineatanarcadegiveschangeintheformof25-centcoins（quarters）andone-dollarbills.Themanagerofthearcadewouldlikeatleast$50worthofquartersand$100worthofone-dollarbillsinthemachineatalltimes.Also,themanagerdoesnotallowmorethan$500inthemachineatanytime.Whatisthemaximumnumberofquartersthemanagerwouldallowinthechangemachine?

A.200

B.400

C.1600

D.2000

CORRECTANSWER:

CDIFFICULTYLEVEL:

2

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

CORRECTANSWER:

ADIFFICULTYLEVEL:

2

6.Acompanysellscandyinjarsthateachhaveavolumeof3cups.Eachjarisfilledaboveacertainline,guaranteeingthatithasmorethan

cupsofcandy.Whichofthefollowinggraphsshowsthepossiblevolumesofcandy,c,incups,acustomermayhave,giventhattheyboughtjjarsofcandy?

A.B.

C.D.

CORRECTANSWER:

BDIFFICULTYLEVEL:

3

7.Inabaseballgame,aplayermusttouch4basestogetarun.However,someplayersget"out"beforereachingthe

base,inwhichcasethebasesdon'tcontributetowardsarun.Letbbethetotalnumberofbasesaplayertouchesinonegameandrbethetotalnumberofrunshegetsfromthosebases.Whichofthefollowinggraphsshowsthepossiblenumberofbasesaplayertouches,giventhenumberofrunshegets?

A.B.

C.D.

CORRECTANSWER:

CDIFFICULTYLEVEL:

3

8.Prachineedsbetween240and260totalfeetoffencepanels.Thehomeimprovementstorehas24short（6-foot）fencepanelsand28long（8-foot）fencepanelsinstock.Whichofthefollowingcombinationsoffencepanelscouldshebuy?

A.6shortfencepanelsand26longfencepanels

B.8shortfencepanelsand23longfencepanels

C.27shortfencepanelsand12longfencepanels

D.30shortfencepanelsand10longfencepanels

CORRECTANSWER:

ADIFFICULTYLEVEL:

3

9.LiQiangislisteningtoasymphonythathas2movements.Thefirstmovementhas3beatspermeasureandthesecondmovementhas4beatspermeasure.Thesymphonyhas446measures.Inanattempttocountthebeats,LiQiangcountsatleastxofthebeatsinthefirstmovementandexactlybbeatsinthesecondmovement.Letxbethenumberofbeatsinthefirstmovementandbbethenumberofbeatsinthesecondmovement.Whichofthefollowinginequalitiesmustbetrue?

A.

B.

C.

D.

CORRECTANSWER:

ADIFFICULTYLEVEL:

3

10.Priyanka'scargetsamaximumof35milespergallon.Accordingtoaparticularconvention,the“wear”onavehicleisatleast

timesthetotalnumberofmilesdrivenplusthetotalnumberofgallonsused.ForPriyanka'scar,letmbethetotalnumberofmilesdriven,letgbethetotalnumberofgallonsused,andletwbethe“wear”.Whichofthefollowingsystemsofinequalitiescorrectlyrepresentstheserelationships?

A.

B.

C.

D.

CORRECTANSWER:

ADIFFICULTYLEVEL:

3

11.

Innightvisiongoggles,lightrayscauseelectronstobeprojectedfromametalsurface.Theaboveequationrelatesthekineticenergyinelectronvolts（eV）,K,ofemittedelectronstothefrequencyinhertz,

ofincidentlightraysandtheworkfunction,

ineV,ofthemetallicsurface.

Inaparticularsetofnightvisiongoggles,theelectronsemittedmusthaveakineticenergyofatleast2.46eV.Ifthefrequencyofincominglightraysislessthan

hertz,whichofthefollowingsystemsofinequalitiesbestmodelstherelationshipbetweentheworkfunction,

andthelightsourcefrequency,

?

A.

B.

C.

D.

CORRECTANSWER:

BDIFFICULTYLEVEL:

2

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.

CORRECTANSWER:

CDIFFICULTYLEVEL:

2

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

CORRECTANSWER:

CDIFFICULTYLEVEL:

2

14.Atechnologystoresellstabletsandcomputers.InJanuarytheysellover300items,andmoreofthosesalesaretabletsthancomputers.InFebruarytheysellexactly100tabletsand20computers.Thegraphatleftshowstwoequationsrelatedtothisproblem,wheretisthetotaltabletsales（inJanuaryandFebruarycombined）,andcisthetotalcomputersales.Whichofthefollowingcombinationscouldbethetechnologystore'stotalsales?

A.240tabletsand100computers

B.360tabletsand180computers

C.240tabletsand260computers

D.120tabletsand180computers

CORRECTANSWER:

BDIFFICULTYLEVEL:

2

15.Elenaisdesigningapaintcanwiththicknesstmillimetersandheighthcentimeters.Shecalculatesthatthethicknessofthecaninmilimetersmustbeatleast0.1timestheheightofthecanincentimetersinordertowithstandpressure.Duetocostconstraints,thecostofmaterialused,（0.2+t+0.5h）cents,mustbeatmost12.2cents.Whichofthefollowingsystemsofinequalitiesbestmodelstherelationshipbetweenheightandthicknessdescribedabove?

A.

B.

C.

D.

CORRECTANSWER:

ADIFFICULTYLEVEL:

2

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

CORRECTANSWER:

ADIFFICULTYLEVEL:

2

17.Aaronispurchasingpartyhatsandfakemustachesforanendoftheschoolyearparty.Hecanspendatmost$30.Fakemustachescost$3each,andpartyhatscost$2each.Ifhemustpurchaseacombinationofatleast15mustachesandpartyhats,whichofthefollowingsystemsofinequalitiesbestmodelstherelationshipbetweenthenumberofmustaches,m,andpartyhats,p,describedabove?

A.

B.

C.

D.

CORRECTANSWER:

ADIFFICULTYLEVEL:

2

18.Acompanymanufacturescellularphonesandlaptopcomputers.Thecompany'sdailyproductionofcellularphones,c,mustbemorethan500,000,anditsdailyproductionoflaptopcomputers,l,mustbemorethan300,000.Ifthemaximumcapacityofthecompany'smanufacturingcenterisnomorethan950,000totalcellularphonesandlaptopcomputers,whichofthefollowingsystemsofinequalitiesbestmodelsthesituationdescribedabove?

A.

B.

C.

D.

CORRECTANSWER:

DDIFFICULTYLEVEL:

2

19.Tonyisraisingfundsforhisschoolsoccerteambysellingboxesofcandyandt-shirts.Hisgoalistomakemorethan$300dollarsoverall.EachboxofcandythatTonysellsearnshim$15,andeacht-shirtsoldearnshim$20.IfTonywantstosell