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?
CC
BY
sab
ianm
aggy
http
s://f
lic.k
r/p/
iV4L
P
1
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
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
2
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.
3
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:
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
4
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?
5