Algebra 1 Real Life of Systems of Linear Equations Project

Transcription

1 Algebra 1 Real Life of Systems of Linear Equations Project Name: Period: Project due date: Project Standards: A.CED.2 Create equations that describe numbers or relationships Create equations in two or more variables to represent relationships between quantities, graph equations on coordinate axes with labels and scales. A.REI.6 Solve systems of equations Solve systems of linear equations exactly and approximately e.g., with graphs), focusing on pairs of linear equations in two variables. F.BF.1 Build a function that models a relationship between two quantities Write a function that describes a relationship between two quantities a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. F.LE.1 Construct and compare linear, quadratic, and exponential models and solve s Distinguish between situations that can be modeled with linear functions and with exponential functions. Project Objectives: The student will show at least 80% mastery in applying systems of linear equations to real life by completing four s from the thirty six attached to this rubric using the three methods of solving linear systems. The student will show creativity and precision to detail to present their four completed s by placing it on a poster or making a book in a manner that is neat, organized and clear. Project Rubric: In order to receive full credit, you must follow the rubric below. Points Earned Possible Points Requirements Comments Complete Four Problems All four s are from different categories All three methods of solving linear systems is used at least once This means one

2 Total: Total: Total: 16 method will be repeated) Graphing Method is placed above the Create equations Graph/Solve The graph is hand drawn using graph paper that is provided X and Y axis are labeled Scale is clear Lines are labeled complete sentences illustrate the word. Substitution Method is placed above the Create Equations Solve complete sentences. illustrate the word.

3 10 Total: Total: 16 Elimination Method is placed above the Create Equations Solve complete sentences. illustrate the word. Fourth Problem Choose one of the three methods is placed above the Create Equations Solve complete sentences. illustrate the word. CHOOSE ONE Poster Board 22x28 inch poster board in any color of choice Divide poster up into four even and clearly distinct cross sections Each section is labeled by the

4 Total: 10 Total: 80 word chosen and the category it came from Make sure your name is on the back of the poster with this rubric attached to it Work is neat and organized Book All paper is the same size Title page with name and class period Table of Contents Either placed in a folder, binder, or any other way you want to present your book. Rubric is at the back of the book Work is neat and organized **Will not be accepted late. If you know you will be gone or have an emergency, please bring it to me early, have a friend bring it in or me esimpson@medford.k12.ma.us

5 RealLifeSystemsofLinearEquationsProject SystemsofLinearEquationsApplicationProblems CoinandMoneyProblems 1) Bobhas60coinsconsistingofquartersanddimes.Thecoinscombinedvalueis$9.45.Findouthowarequarters andhowmanyaredimes. 2) Erichas130coinsconsistingofnickelsandquarters.Thecoinscombinedvaluecomesto$15.90.Findouthow manyofeachcoinerichas. 3) Aliceiscountingacashregisterattheendofthenight.Shehas$1015in$5billsand$10bills.Ifshehas138bills alltogether,howmanyofeachtypedoesshehave? 4) Maxhas250dimesandquartersworthoftotalof$39.25.Findouthowmanyofeachkindofcoinhehas. 5) Dominichas24coinsinhalfAdollarsanddimes.Theirtotalvalueis$3.60.Howmanycoinsofeachtypedoeshe have? 6) Joshhasabundleofmoneyconsistingof$1billsand$5bills.Thereare62billsinthebundle.Thetotalvalueof thebundleis$230.findthenumberof$1billsandthenumberof$5bills. TicketProblemsandSimilar 7) 353peopleattendalocalplayataprivateclub.Membersgetticketsfor$2.75,whilenonAmembershavetopay $6.50.Ifthetotalgatefortheplaycameto$1762,howmanymembersandnonAmemberscametotheplay? 8) Jimrunsafoodcartandduringabusyoutdoorfestivalhesold$ worthoffood.Hesellshotdogsfor $2.95andsteaksandwichesfor$9.95.Ifhesoldatotalof985itemsthatday,howmanyofeachitemdidhe sell? 9) 586peopleattendabanquetatDisney.Residentspaid$12.95andnonAresidentspaid$17.95.IfDisneymade $ fromticketsalesfortheevent,howmanyresidentsandnonAresidentsattended? 10) AshleyandMikearesellingcheesecakesforaschoolfundraiser.CustomerscanbuyNewYorkstylecheesecakes andstrawberrycheesecakes.ashleysold9newyorkstylecheesecakesand12strawberrycheesecakesfora totalof$276.mikesold3newyorkstylecheesecakesand1strawberrycheesecakeforatotalof$41.whatis thecosteachofonenewyorkstylecheesecakeandonestrawberrycheesecake? 11) ShawnissellingticketstotheMr.MHSshow.Onethefirstdayofticketsalestheschoolsold1adultticketand 11studentticketsforatotalof$79.Theschooltookin$162ontheseconddaybyselling6adultticketsand14 studenttickets.whatisthepriceofeachofoneadultticketandonechildticket? 12) DanielandLaceyeachimprovedtheiryardsbyplanningtulipsandsunflowers.Theyboughttheirsuppliesfrom thesamestore.danielspent$12on1tulipand1sunflower.laceyspent$60on4tulipsand10sunflowers. Whatisthecostofonetulipandonesunflower? 13) YellowstoneNationalParkisapopularfieldtripdestination.ThisyeartheseniorclassatHighSchoolAandthe seniorclassathighschoolbbothplannedtripsthere.theseniorclassathighschoolarentedandfilled2vans and10busseswith616students.highschoolbrentedandfilled8vansand9busseswith635students.every vanhadthesamenumberofstudentsinit.everybushadthesamenumberofstudentsinit.howmany studentscanavancarry?howmanystudentscanabuscarry?

6 BankAccountProblems 14) Janeinvests$9885intotwoaccounts.Asavingsaccountearns6%interest,whileamoneymarketaccountearns 9.5%interest.Afteroneyearshemade$696.35interestfrombothaccounts.Howmuchdidsheinvestintoeach account? 15) Ralphinvests$15,600intotwodifferentaccounts;asavingsaccountandcheckingaccount.Thesavingsaccount earns8%interestandthecheckingearns9%.after1yearhehasearned$ interest.howmuchdidralph investintoeachaccount? 16) Agroupinvested$20440intotwoaccounts.Asecurebondaccountearned2.5%interestandamoreriskystock ventureaccountearned3.4%interest.thegroupearned$623.05fortheinvestmentinoneyear.howmuchdid thegroupinvestintoeachaccount? 17) Nateinvested$12000intwobankaccounts.Oneaccountpays6%annualinterest,andtheotheraccountpays 5%annualinterest.Ifthecombinedinterestearnedinbothaccountsafterayearwas$700,howmuchmoney wasinvestedineachaccount? MixtureProblems 18) Louwantstomakeacoffeemixturetosell.HeisgoingtomixSumatracoffeewhichcosts$2.50perpoundwith Columbiancoffeewhichcosts$3.75perpound.Hewantstomake50poundsofmixandhewantsthecostof themixtobe$3.35perpound.howmanypoundofeachwillheneed? 19) Jackiewantstomakeamixtureofnutstosellinherstoreconsistingofhazelnutsandcashews.Hazelnutscost $6.50perpoundandcashewscost$4.50perpound.IfJackiewants60poundstotalofmixtureandthecostto be$5.10perpound,howmanypoundsofeachwillsheneed? 20) Inacandyshop,chocolatewhichsellsfor$4apoundismixedwithnutswhicharesoldfor2.50apound.The chocolateanutcandysellsfor$3.50apound.howmuchofeachareusedtomake30poundsofthemixture? 21) Howmanyouncesof20%hydrochloricacidsolutionand70%hydrochloricacidsolutionmustbemixedtoobtain 20ouncesof50%hydrochloricacidsolution? 22) Afarmerhastwotypesofmilk,onethatis24%butterfatandanotherwhichis18%butterfat.Howmuchofeach shouldheusetoendupwith42gallonsof20%butterfatmilk? Distance,RateandTimeProblems 23) Aplanecantravel1,015milesin7hourstravelingagainstthewind.Travelingwiththesamewind,theplanecan travel820milesin4hours.howfastcantheplanetravelinstillairandhowfastisthewindcurrent? 24) LanceArmstrongcanride162milesonflatgroundin6hourswithagoodbreezeathisback.Ittakeshim10 hourstogo90mileswiththesamebreezeworkingagainsthim.howfastislancegoingonabikeandhowfast isthewindspeed? 25) IttakesBobtheBoyScout10hourstopaddleupstreamagainstthecurrent)adistanceof15miles.Whenhe turnsaroundhefindsitonlytakeshim5hourstopaddle22.5mileswiththecurrent.howfastisbob sboat goinginstillwaterandwhatisthespeedofthecurrentoftheriver? 26) FlyingfromTokyotoLondonisapproximately6175miles.OnthewaytoLondonfromTokyoagainstthewind) theflighttook13hours.thereturnflightwiththewind)took9.88hours.findthespeedoftheplaneinstillair andthespeedofthewindcurrent.

7 27) Travelingdownstreamacertainboatwent22km/h.Travelingupstreamitwentonly4km/h.Findthespeedof theboatinstillwaterandthespeedofthecurrent. 28) Flyingwiththewindaplanewent413mph.Flyingintothesamewindtheplaneonlywent351mph.Whatisthe speedofthewind?howfastwouldtheplanegoiftherewerenowind? 29) Goingdowntheriverthecrewteamrowed15mph.Goingbackuptheriveritonlywent1mph.Findthespeed oftheboatinstillwaterandthespeedofthecurrent. Miscellaneous 30) Bobate10carrotsand7Hershey skissesandthetotalcalorieswere263.fredate4carrotsand8hershey s kissesandthetotalcalorieswere230.howmanycaloriesareinacarrotandahershey skiss?theanswerisnot ascientifictruth,onlymadeupnumbers!!!) 31) DuringaTechnoAGeekAStoresale6blankvideotapesand12blankDVD scost$35.10.duringthesamesale,8 blankvideotapesand3blankdvd scost$27.95.whatwasthecostofablankvideotapeandthecostofablank DVD? 32) 40adultsand26kidswenttoseeamovieontheopeningscreeningandtherevenuefortheshowingwas $ Thenextshowing20adultsand31kidswenttoseethesamemovieandtherevenuewas$ Howmuchwasanadultticketandhowmuchwasakidticket? 33) OnonedayFred ssportsworldsold9pittsburghsteelersjerseysand3clevelandbrownsjerseysforatotalof $ Thenextdaytheysold12Steelersjerseysandonly2Brownsjerseysforatotalof$ Howmuch isthesteelersjerseyandhowmuchisthebrownsjersey? 34) Findthevalueoftwonumbersiftheirsumis19andtheirdifferenceis5. 35) Thedifferenceoftwonumbersis1.Theirsumis25.Whatarethenumbers? 36) ThesumofthedigitsofacertaintwoAdigitnumberis2.Reversingitsdigitsdecreasesthenumberby18.Whatis thenumber?