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.

CC

BY

Der

ek H

atfie

ld

http

s://f

lic.k

r/p/

eU3s

8f

14

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

15

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

16