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1、2008AMC12AProblemsProblem1Abakeryownerturnsonhisdoughnutmachineat.Atthemachinehascompletedonethirdoftheday'sjob.Atwhattimewillthedoughnutmachinecompletethejob?SolutionThemachinecompletesone-thirdofthejobinhours.Thus,theentirejobiscompletedinhours.Sincethemachinewasstar
2、tedat,thejobwillbefinishedhourslater,at.Theansweris.Problem2Whatisthereciprocalof?Solution.Problem3Supposethatofbananasareworthasmuchasoranges.Howmanyorangesareworthasmuchasofbananas?SolutionIf,then.Problem4WhichofthefollowingisequaltotheproductSolutionSolution1.Soluti
3、on2Noticethateverythingcancelsoutexceptforinthenumeratorandinthedenominator.Thus,theproductis,andtheansweris.Problem5Supposethatisaninteger.Whichofthefollowingstatementsmustbetrueabout?SolutionFortobeaninteger,mustbeeven,butnotnecessarilydivisibleby.Thus,theansweris.Pr
4、oblem6Heathercomparesthepriceofanewcomputerattwodifferentstores.Storeoffersoffthestickerpricefollowedbyarebate,andstoreoffersoffthesamestickerpricewithnorebate.Heathersavesbybuyingthecomputeratstoreinsteadofstore.Whatisthestickerpriceofthecomputer,indollars?SolutionSol
5、ution1Letthestickerpricebe.Thepriceofthecomputerisatstore,andatstore.Heathersavesatstore,so.Solving,wefind,andthethusansweris.Solution2Theinstoreisbetterthantheadditionaloffatstore.Thustheoffisequalto,andthereforethestickerpriceis.Problem7WhileSteveandLeRoyarefishing1m
6、ilefromshore,theirboatspringsaleak,andwatercomesinataconstantrateof10gallonsperminute.Theboatwillsinkifittakesinmorethan30gallonsofwater.Stevestartsrowingtowardtheshoreataconstantrateof4milesperhourwhileLeRoybailswateroutoftheboat.Whatistheslowestrate,ingallonsperminut
7、e,atwhichLeRoycanbailiftheyaretoreachtheshorewithoutsinking?SolutionItwilltakeofanhourorminutestogettoshore.Sinceonlygallonsofwatercanentertheboat,onlynetgallonscanentertheboatperminute.Sincegallonsofwaterentertheboateachminute,LeRoymustbailgallonsperminute.Problem8Wha
8、tisthevolumeofacubewhosesurfaceareaistwicethatofacubewithvolume1?SolutionAcubewithvolumehasasideoflengthandthusasurfa
