SECONDARY MATH I // MODULE 5

SYSTEMS OF EQUATIONS AND INEQUALITIES – 5.1

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5. 1 Pet Sitters

A Develop Understanding Task

TheMartineztwins,CarlosandClarita,aretryingtofindawaytomakemoneyduring

summervacation.Whentheyoverheartheirauntcomplainingabouthowdifficultitistofind

someonetocareforherpetswhileshewillbeawayonatrip,CarlosandClaritaknowtheyhave

foundtheperfectsolution.Notonlydotheyhavealarge,unusedstorageshedontheirproperty

wheretheycanhouseanimals,theyalsohaveaspaciousfencedbackyardwherethepetscanplay.

CarlosandClaritaaremakingalistofsomeoftheissuestheyneedtoconsideraspartof

theirbusinessplantocareforcatsanddogswhiletheirownersareonvacation.

• Space:Catpenswillrequire6ft2ofspace,whiledogrunsrequire24ft2.CarlosandClaritahaveupto360ft2availableinthestorageshedforpensandruns,whilestillleavingenoughroomtomovearoundthecages.

• Start-upCosts:CarlosandClaritaplantoinvestmuchofthe$1280theyearnedfromtheirlastbusinessventuretopurchasecatpensanddogruns.Itwillcost$32foreachcatpenand$80foreachdogrun.

Ofcourse,CarlosandClaritawanttomakeasmuchmoneyaspossiblefromtheirbusiness,

sotheyaretryingtodeterminehowmanyofeachtypeofpettheyshouldplantoaccommodate.

Theyplantocharge$8perdayforboardingeachcatand$20perdayforeachdog.

Aftersurveyingthecommunityregardingthepetboardingneeds,CarlosandClaritaare

confidentthattheycankeepalloftheirboardingspacesfilledforthesummer.

Sothequestionis,howmanyofeachtypeofpetshouldtheypreparefor?Theirdadhas

suggestedthesamenumberofeach,perhaps12catsand12dogs.Carlosthinkstheyshouldplan

formoredogs,sincetheycanchargemore.Claritathinkstheyshouldplanformorecatssincethey

takelessspaceandtime,andthereforetheycanboardmore.

Whatdoyouthink?WhatrecommendationswouldyougivetoCarlosandClarita,andwhat

argumentwouldyouusetoconvincethemthatyourrecommendationisreasonable?

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SECONDARY MATH I // MODULE 5

SYSTEMS – 5.1

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5.1

READY Topic:Solvingsystemofequationsbygraphing.Substitutethegivenpointsintobothequationstodeterminewhichorderedpairsatisfiesthesystemoflinearequations.Graphbothequationsandlabelthepointofintersectiontoverifythesolution.

1.! = 3! − 2 !"# ! = ! 2.! = 2! + 3 !"# ! = ! + 5 a. 0,−2 a.(2,7)b. 2, 2 b.(-7,11)c. 1, 1 c.(0,5)

Solvethefollowingsystemsbygraphing.Checkthesolutionbyevaluatingbothequationsatthepointofintersection.

3.! = ! + 3 !"# ! = −2! + 3 4.! = 3! − 8 !"# ! = −!

READY, SET, GO! Name PeriodDate

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SECONDARY MATH I // MODULE 5

SYSTEMS – 5.1

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5.1

SET Topic:Determiningpossiblesolutionstoinequalities

5.Atheaterwantstotakeinatleast$2000forthematinee.Children’sticketscost$5eachandadultticketscost$10each.Thetheatercanseatupto350people.Findfivecombinationsofchildrenandadultticketsthatwillmakethe$2000goal.

6.TheUtahJazzscored102pointsinarecentgame.Theteamscoredsome3-pointshots,2-pointshots,andmanyfreethrowsworth1-pointeach.Findfivecombinationsofbasketsthatwouldaddupto102points.

7.Useasmanyofthefollowingshapesinanycombinationasyouneedtotrytofillinasmuchofthe12by12gridasyoucan.Youmayrotateorreflectashapeifithelps.Writeyouranswershowinghowmanyofeachshapeyouusedusingthelettersthatidentifyshape.

Example:3a,5b,10c,2d,6ea.b.c.d.e.

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SECONDARY MATH I // MODULE 5

SYSTEMS – 5.1

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5.1

GO Topic:Graphinglinearequationsanddeterminingifagivenvalueisasolution,arithmeticsequences

Grapheachequationbelow;thendetermineifthepoint(3,5)isasolutiontotheequation.Findtwopointsotherthan(3,5)thataresolutionstotheequation.Showthesepointsonthegraph. 8.! = 2! − 1

9.! = !! ! + 2

10.! = −3! + 5

11.! = !!! ! + 4

Thetablesbelowrepresentdifferentarithmeticsequences.Fillinthemissingnumbers.Thenwritetheexplicitequationforeach.12.term(x) 1 2 3 4value(y) 17 -7Equation:

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SECONDARY MATH I // MODULE 5

SYSTEMS – 5.1

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5.1

13.term(x) 1 2 3 4 5 6 7 8 9 10 11 12 13term(y) 17 -7Equation:14.term(x) 1 2 3 4 5 6 7value(y) 17 -7Equation:15.Eachofthesequencesabovebeginsandendswiththesamenumber.Wouldthegraphofeach

sequencerepresentthesameline? Justifyyourthinking.16.Ifyougraphedeachofthesesequencesandmadethemcontinuousbyconnectingeachpoint,

wherewouldtheyintersect?

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