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SECONDARY MATH I // MODULE 5
SYSTEMS OF EQUATIONS AND INEQUALITIES – 5.4
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5. 4 Pampering and Feeding Time
A Practice Understanding Task
CarlosandClaritahavebeenworriedaboutspaceandstart-upcostsfortheirpetsitters
business,buttheyrealizetheyalsohavealimitontheamountoftimetheyhavefortakingcareof
theanimalstheyboard.Tokeepthingsfair,theyhaveagreedonthefollowingtimeconstraints.
• FeedingTime:CarlosandClaritaestimatethatcatswillrequire6minutestwiceaday—
morningandevening—tofeedandcleantheirlitterboxes,foratotalof12minutesperdayforeachcat.Dogswillrequire10minutestwiceadaytofeedandwalk,foratotalof20minutesperdayforeachdog.Carloscanspendupto8hourseachdayforthemorningandeveningfeedings,butneedsthemiddleofthedayoffforbaseballpracticeandgames.
• PamperingTime:Thetwinsplantospend16minuteseachdaybrushingandpettingeachcat,and20minuteseachdaybathingorplayingwitheachdog.Claritaneedstimeoffinthemorningforswimteamandeveningforherartclass,butshecanspendupto8hoursduringthemiddleofthedaytopamperandplaywiththepets.
Writeinequalitiesforeachoftheseadditionaltimeconstraints.Shadethesolutionsetfor
eachconstraintonseparatecoordinategrids.
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SECONDARY MATH I // MODULE 5
SYSTEMS – 5.4
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.4
READY Topic:Writinglinearequationsinstandardformandslope-interceptform.Rewritethegivenequationsothattheyareinslope-interceptform. ! = !" + !
1.7! − 14! = −56 2.−8! − 2! = 6 3.15! + 9! = 45Rewritethegivenequationssothattheyareinstandardform.(Ax+By=C,whereA,B,andCarewholenumbersandAispositive.)
4.! = 7! − 3 5.! = 2! + 9 6.! = −4! − 11
7.! = !! ! + 8 8.! = !! ! − 2 9.! = − !! ! + !!
SETTopic:Writinginequalitiesfromarealworldproblem.Graphinginequalities.
10.Onafinalforacreativewritingcourse,Benwasrequiredtowriteacombinationofatleast10poemsorparagraphs.Benknewthateachpoemwouldtakehim30minutestowritewhileaparagraphwouldonlytake10minutes.Benwasgiventwohourstocompletetheexam.
a.Writeaninequalitytomodeleachconstraint.(Hint:Oneconstraintistimeandtheotheristhenumberofneededitems.Letxbethenumberofpoemswrittenandybethenumberofparagraphswritten.)
b.Grapheachinequalityonaseparatecoordinategridandshadethesolutionsetforeach.
READY, SET, GO! Name PeriodDate
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SECONDARY MATH I // MODULE 5
SYSTEMS – 5.4
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.4
GO Topic:Substitutingavaluetocheckifit’sasolution
Determinewhether! = !isasolutiontoeachproblem.11. 3 ℎ − 4 = −3 12. 3ℎ = 2 ℎ + 2 − 113. 2ℎ − 3 = ℎ + 6 14. 3ℎ > −3
15. !! ≤ ℎ × !! 16. !
! > ℎ × !! Determinethevalueof!thatmakeseachequationtrue. 17. 4! − 2 = 8 18. 3 ! + 5 = 20
19. 2! + 3 = 2! − 5 20. 4 6! − 1 = 3 8! + 5 − 19
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