4Linearinequalitywordproblems1文档格式.docx

4Linearinequalitywordproblems1文档格式.docx

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1.25

Correctanswer:

BDifficultylevel:

2

2.Therabbitpopulationinanisolatedforestrisesandfallsdependingonthepopulationofpredators.Withintheyear2014,thepopulation,p,inthousandsofrabbitsmmmmonthsafterJanuary1,2014is:

p=0.05（m−1.5）（m−8.5）+10

ThepopulationreachedtenthousandsometimeinFebruary.Atwhatothertime,givenasmonthsafterJanuary1,2014,didtherabbitpopulationreachtenthousand?

8.5Difficultylevel:

3.The"

hangtime"

ofafootballistheamountoftimethefootballstaysintheairafterbeingkicked.Theheight,inmeters,ofthefootballabovethegroundattimetcanbemodeledbythequadraticfunction:

Whichofthefollowingequivalentexpressionsdisplaysthehangtimeofthefootballasaconstantorcoefficient?

C.

D.

4.Kaiathrowsastoneverticallyupwardfromabridge.Theheight,inmeters,ofthestoneabovethewaterattimetcanbemodeledbythequadraticfunction:

Afterhowmanysecondsdoesthestonehitthewater?

A.1second

B.2seconds

C.4seconds

D.8seconds

CDifficultylevel:

5.Morethan450studentstraveledtoastateparkforafieldtrip.Theschoolallowed6studentstotravelbycar,andtheresttraveledon11buses,eachofwhichheldthesamenumberofstudents.Ifthereweresstudentsineachbus,whichinequalitybestrepresentsthissituation?

ADifficultylevel:

6.Abarbercharges$12forahaircut.Hisoperatingexpensesare,onaverage,$37perday.Hecalculateshisprofitbysubtractinghisoperatingcostsfromthemoneyheearnsfromthehaircutshegives.Inagivenday,thebarberexpectstomakeaprofitofatleast$86.Ifthebarbergiveshhaircutsinaday,whichinequalitybestmodelsthissituation?

7.AdistributorshipsDVDstoseveralstores.TheshippingboxescontainseveralDVDs（intheircases）plusalayerofpaddingateachendofthebox.TheDVDcasesandlayersofpaddingcanbearrangedneatlyinsideeachbox.EachDVDcaseis14mm（millimeters）thick,eachlayerofpaddingis10mmthick,andthelengthoftheinterioroftheboxis132mm.IfdrepresentsthenumberofDVDsthatthedistributorcanfitintooneboxwithtwolayersofpadding,whichofthefollowinginequalitiesbestmodelsthesituation?

8.Torentacarforoneweek,acarrentalcompanychargesa$200basepriceaswellas$0.45permile.Jenniferwillrentavehicleatthiscompany,butshehasa$275budget.WhichofthefollowingisapossiblenumberofmilesthatJennifercandrivewithoutexceedingherbudget?

A.166miles

B.167miles

C.168miles

D.169miles

9.Woo-Jinwouldliketobringseveralbooksfromhisfavoriteseriesinhisbackpack.Thebackpackcanholduptoadepthof

inchesofmaterials.Woo-Jin'

slaptopandanotebookfillatotalof3inchesofthatdepth.Eachbookwouldfill1.5inchesofthedepthofthebackpack.Onlyonestackofbookscanfittheheightandwidthofthebackpack.IfxrepresentsthenumberofbooksthatWoo-Jincouldcarryinhisbackpack,whichofthefollowinginequalitiesbestmodelsthesituationdescribedabove?

10.Intheyear2000,theaverageAmericanconsumed8.3gallonsofwholemilkperyear.Thisamounthasbeendecreasingby0.3gallonsperyear.Whichinequalitycanbeusedtofindthenumberofyears,t,since2000whenwholemilkconsumptionwasgreaterthan6.0gallonsperpersonperyear?

3

11.Anamusementcenterchargesa$45flatfeeforanybirthdaypartyplus$3.50foreachguestafterthefirstone.Josiahwantstospendnomorethan$200forhisbirthdayparty.Iftherearexguests,whichofthefollowinginequalitiesbestmodelsthesituationabove?

12.Hamadiisrentingacar.Withhisextremecoupons,therentalchargeis$17.50perdayplus$0.16permile.HiscompanywillreimburseHamadifor$33ofthisportionofthetravelexpenses.Ifherentsthecarforoneday,whatisonepossiblenumberofmilespaidforbythecompany?

A.53

B.97

C.110

D.150

13.Togettoschool,Da'

Quonwalks0.6milesfromhishousetothebusstop.Hethentakesthebusfor3.9miles.Afterhegetsoffthebus,hecanchooseoneofseveralwalkingroutestoschool.Thetotalamountofmileshetravels,viawalkingandbus,doesnotexceed5.4.Whatisthegreatestpossiblenumberofmileshewalksaftergettingoffthebus?

A.0.0miles

B.0.3miles

C.0.9miles

D.1.5miles

14.Karimhasa$35giftcardtohisfavoriterestaurant.Mealtaxinhisareais14.3%.Karimwouldalsoliketoleavea$5tip.IfcrepresentsKarim'

spre-taxbill,andhewantstopaytheentiremealamount,includingtipandtax,usingthegiftcard,whichofthefollowinginequalitiesbestmodelsthesituationdescribedabove?

15.Oneoftherulesinapublicspeakingcontestrequirescontestantstospeakforascloseto3minutes（180seconds）aspossible.Contestantslose2pointsforeachsecondtheyspeakeitheroverorunderthe3minutes.Ifacontestantlost18points,whatarethepossiblelengthsoftimetheyspoke?

A.171andseconds

B.174andseconds

C.171andseconds

D.174andseconds

1

16.Agemologistdeterminesthatagemstoneweighs1.235carats.Guidelinesallowamaximumweighingerrorof0.001caratsinreportinggemstoneweight.Whichofthefollowingequationscanbeusedtodeterminethesmallestandlargestpossibletrueweights,c,ofthegemstone?

DDifficultylevel:

17.Acompany'

sunitcostforproducingxunitsisaminimumwhenx=2,000unitsareproduced.Theunitcostincreases$0.25foreveryunitmoreorlessthan2,000produced.Whichofthefollowingcouldbethenumberofunitsforwhichtheunitcostincreasesby$7.50fromtheminimum?

A.1,700or2,300

B.1,975or2,025

C.1,997or2,003

D.1,970or2,030

18.Felipehasa15gallongastankinhiscar.Hefillshistank,andthendrivesthexmilesbacktocollege.Uponhisarrival,hefillshistankfor$20.91.Ifhiscaraverages24milespergallon（mpg）,andatthetime,gascosts$2.46pergallon,whichofthefollowingbestapproximatesx?

A.128

B.204

C.360

D.502

19.In2005,approximately16.5%ofseatsinnationalparliamentswereheldbywomen.Between2005and2014,thispercentageincreasedataconstantrateofabout3percentagepointsevery5years.Iftistheyearwhenapproximately19%oftheseatsinnationalparliamentswereheldbywomen,whichofthefollowingequationsbestmodelsthesituation?

20.Ellaneedsa70%isopropylalcoholsolutionasanantiseptic.Shehasa100milliliter（ml）containerof90%isopropylalcoholsolution.ApproximatelyhowmuchwatershouldEllaaddtodiluteittoa70%isopropylalcoholsolution?

Roundtothenearesttenth.

mlofwater

Correctanswer:

28.6Difficultylevel:

21.Formanytrees,theapproximateageofthetree（inyears）isequaltothediameterofthetree（ininches）timesthetree'

sgrowthfactor.Denizestimatesthatacertainredmapletreeinheryardisabout80yearsold.Ifredmapletreeshaveagrowthfactorof4.5,whichofthefollowingequationscouldbeusedtofindx,thediameterofthetreeinfeet?

22.Thepropertytaxesinatowndecreaseasthedistancefromthetownhallincreases.Forevery5milesfromthetownhall,propertytaxesdecreaseby0.2percentagepoints.Whichofthefollowingequationscanbeusedtodeterminehowfarnorthorsouthofthetownhallahouseiswhosepropertytaxesare0.76percentagepointslessthanthetaxesatthetownhall?

Note:

yisthepositionofahousethatisdirectlynorthorsouthofthetownhall,withy>

0representingnorthandy<

0representingsouth.

23.Josie'

shaircurrentlyfallsabout16centimeters（cm）belowhershoulderandgrowsabout5cmevery4months.Josieplanstogrowherhairanddonateabout21cmofherhairtocharityafterhernexthaircut.IfJosiewouldliketohaveherhairfallabout5cmbelowhershouldersafterhernexthaircut,whichofthefollowingequationscouldbeusedtofindthenumberofmonths,mmm,forwhichJosiemustgrowherhair?

24.Melissahasan80inch（in）pieceofwroughtironthatshewishestousetomakearectangularpieceofart.Shewantsthelengthoftherectangularpieceofarttobe12incheslongerthanthewidth.Whatisthelargestlengthpossible?

A.14in

B.26in

C.34in

D.46in

25.Yongneedstocuta3footlongboardintoseveral2inchlengths.Witheachcut,hissawbladeshavesoffanadditional

inchoftheboard.Whatisthemaximumnumberoffull2inchlengthsthatYongcancutfro