9 LO2 Multiple Graphs

8/4/2019 9 LO2 Multiple Graphs

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Grade 12 Mathematical Literacy

LO2 Multiple graphs: Graphs with two or more linearfunctions and graphs with linear and non-linearfunctions.

1. Mrs Radebe decides that it is time for her teenage twins to havecellular telephones so that they will be able to contact her aftertheir soccer practices and matches. She approaches two cellulartelephone companies in order to determine the best deal that shecan get. She is aware that the boys will not only use theirtelephone to telephone her, but that they would also use them tocontact their friends, go on line and probably also use smss. Shetabulates the information she has found as follows:

Cellphoneprovider Contract

Pay-as-you-go

BasicRate

Cost perMinute -peak

Cost perMinute - offpeak

Cost perMinute

YellowPhoneCompany

R95 permonth R2,65

First 50minutesfree; R1,90after 50minutes R2,50

RedPhoneCompany

R110permonth R2,65

First 85minutesfree; R1,25after 85minutes R2,45

1.1 Take the above information into account todetermine the cost of giving the twins each acellphone by copying and completing the tablebelow.

Maths & Science Marketing
http://images.google.co.za/imgres?imgurl=http://onemansblog.com/wp-content/uploads/2006/10/razr.jpg&imgrefurl=http://onemansblog.com/2006/10/04/a-guide-to-free-internet-phone-calls/&h=305&w=325&sz=20&hl=en&start=3&tbnid=cWVasovwTe3uyM:&tbnh=111&tbnw=118&prev=/images%3Fq%3Dcellular%2Btelephone%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG


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Number ofminutes

YellowPhoneCompany

ContractPeaktime

YellowPhoneCompany

ContractOff peaktime

YellowPhoneCompany -

Pay-as-you-goPeak time

RedPhone

Company PrepaidPeak time

Red PhoneCompany ContractOff peak

time

Red PhoneCompany -

Pay-as-you-go offpeak time



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10

20

30

40

5060

70

80

90

100

110

120

130140

150

1.2 Use a set of axis, with the number of minutes on the x-axis andthe cost on the y-axis, and plot and join the points in the abovetable.

1.3 Which option would you recommend for Mrs Radebe. Explain.

http://images.google.co.za/imgres?imgurl=http://handcellphone.com/wp-content/themes/green-marinee/phonepic/Oxyon-cell-phone.jpg&imgrefurl=http://www.handcellphone.com/archives/benqsiemens-secret-project-oxyon-cellular-phone&h=302&w=267&sz=10&hl=en&start=33&tbnid=8oC2S0mNqkqkDM:&tbnh=116&tbnw=103&prev=/images%3Fq%3Dcellular%2Btelephone%26start%3D18%26gbv%3D2%26ndsp%3D18%26svnum%3D10%26hl%3Den%26sa%3DN


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2. Zanele wants to rent a car while in Johannesburg for a week. Sheobtains the following three quotes from three car rental companies.

Company Type of Car Daily rental

rate

Free kms Cost per km

for excesskms

Budget Tazz R295 Unlimited -

Avis Polo Playa R220 200 km R1,50

Value Tazz R245 200 km R1,05

2.1 Copy and complete the table below.

Kms 0 km 100 km 150 km 200 km 250 km 300 km

Budget

Avis

Value

2.2 Represent the information in 2.1 above graphically on a set ofaxes.

2.3 If Zanele travels 245 kms per day, which option would be thecheapest?

2.4 If Zanele travels less than 50 kms per day, which option would

be the cheapest?

2.5 If Zanele travels between 50 and 200 kms per day, whichoption would cost the most?

http://images.google.co.za/imgres?imgurl=http://www.capecorporate.co.za/images/fleet_tazz.jpg&imgrefurl=http://www.capecorporate.co.za/fleet_budget.php&h=125&w=254&sz=10&hl=en&start=8&tbnid=DEJgWn3P7iH89M:&tbnh=55&tbnw=111&prev=/images%3Fq%3Dtoyota%2Btazz%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DGhttp://images.google.co.za/imgres?imgurl=http://www.taxinet.co.za/images/tazz.gif&imgrefurl=http://www.taxinet.co.za/ourfleet.htm&h=150&w=200&sz=13&hl=en&start=28&tbnid=PKm1RnUnydU2HM:&tbnh=78&tbnw=104&prev=/images%3Fq%3Dtoyota%2Btazz%26start%3D18%26gbv%3D2%26ndsp%3D18%26svnum%3D10%26hl%3Den%26sa%3DNhttp://images.google.co.za/imgres?imgurl=http://www.solmar.es/imagenes/vehiculos/POLO2.jpg&imgrefurl=http://www.solmar.es/alquilerdecoches/turismos.php&h=201&w=300&sz=23&hl=en&start=7&tbnid=_PIm-AU-jgNSNM:&tbnh=78&tbnw=116&prev=/images%3Fq%3Dvolkswagen%2Bpolo%2Bplaya%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG


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3. Inflation has resulted in escalated costs for all aspects of theeconomy. Building costs have also escalated over the past fewyears. When you want to build a house the quote given to you bythe builder will be given as a rate in rand per square metre (R/m).Refer to the table below and answer the questions that follow.

Year 2004 2005 2006 2007

Cost Per m R3 000 R3 300 R3 712,50 R4 455

3.1 Determine the cost of building a 80m house in3.1.1 20043.1.2 20053.1.3 20063.1.4 2007

3.2 Determine the cost of building a 190m house in3.2.1 20043.2.2 20053.2.3 20063.2.4 2007

3.3 Use a set of axes with the m on the x-axis and the cost on the y-axis. Plot the amounts of 3.1.1 above and 3.2.1 above on the setof axes and join the points. Now repeat the process for eachyear.

3.4 Read off from your graph what the cost would be of a 120mhouse in 2007.

http://images.google.co.za/imgres?imgurl=http://www.gpch.org/CampusMaps/SANCmap.JPG&imgrefurl=http://www.gpch.org/CampusMaps/Sancbdg.asp&h=446&w=380&sz=77&hl=en&start=7&tbnid=JB5BzpoXsnROsM:&tbnh=127&tbnw=108&prev=/images%3Fq%3Dbuilding%2Bhouses%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DGhttp://images.google.co.za/imgres?imgurl=http://www.aswcc.arkansas.gov/NPS_Webpage/images/sediment%2520nps%2520residence%2520construction.jpg&imgrefurl=http://www.aswcc.arkansas.gov/NPS_Webpage/NPS%2520Sources.htm&h=390&w=553&sz=68&hl=en&start=2&tbnid=vB5x2NgyStBcJM:&tbnh=94&tbnw=133&prev=/images%3Fq%3Dconstruction%2Bsites%26gbv%3D2%26ndsp%3D18%26svnum%3D10%26hl%3Den%26sa%3DNhttp://images.google.co.za/imgres?imgurl=http://www.californiaaircontrol.com/nss-folder/pictures/construction.jpg&imgrefurl=http://www.californiaaircontrol.com/services1/&h=272&w=400&sz=28&hl=en&start=52&tbnid=Qks0_xDeJq1DxM:&tbnh=84&tbnw=124&prev=/images%3Fq%3Dconstruction%2Bsites%26start%3D36%26gbv%3D2%26ndsp%3D18%26svnum%3D10%26hl%3Den%26sa%3DN


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A NSWERS

1.1

Numberofminutes

YellowPhoneCompany

PrepaidPeaktime

YellowPhoneCompany- PrepaidOff Peaktime

Yellow

PhoneCompany- Pay-as-you-goPeaktime

RedPhoneCompany- PrepaidPeak time

RedPhoneCompany

PrepaidOff peaktime

RedPhoneCompany- Pay-as-you-go offpeak time

10 121.5 95 25 136.5 110 24.5

20 148 95 50 163 110 49

30 174.5 95 75 189.5 110 73.5

40 201 95 100 216 110 9850 227.5 95 125 242.5 110 122.5

60 254 114 150 269 110 147

70 280.5 133 175 295.5 110 171.5

80 307 152 200 322 110 196

90 333.5 171 225 348.5 116.25 220.5

100 360 190 250 375 128.75 245

110 386.5 209 275 401.5 141.25 269.5

120 413 228 300 428 152 294130 439.5 247 325 454.5 166.25 318.5

140 466 266 350 481 178.75 343

150 492.5 285 375 507.5 191.25 367.5

http://images.google.co.za/imgres?imgurl=http://www.iaei.org/subscriber/magazine/01_f/geyer_ph4.gif&imgrefurl=http://www.iaei.org/subscriber/magazine/01_f/geyer.htm&h=432&w=400&sz=45&hl=en&start=6&tbnid=Zt48cBXxFX5ZIM:&tbnh=126&tbnw=117&prev=/images%3Fq%3Dcellular%2Btelephones%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG


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1.2

Comparison of Cellphone options

0

100

200

300

400

500

600

10 30 50 70 90 110

130

150

Time in minutes

Costofcontract

Yellow Contract Peak

Yellow Contract off peak

Yellow Pay as you go

Red Contract Peak

Red Contract off peak

Red Pay as you go

1.3 The cheapest option would be to use the Red Phone Companysoffer of a contract with off-peak minutes. This is the cheapestoption. However, she will not be able to dictate that the twins onlyuse off peak minutes, so it may be more advisable for her to getuse the Red Phone Companys pay as you go option. This way

she can dictate the amount of money she gives the twins and it willbe the cheapest option financially if they do not only stick to offpeak times.

http://images.google.co.za/imgres?imgurl=http://www.digit-life.com/articles/digestmobile0105/pic6.jpg&imgrefurl=http://www.digit-life.com/articles/digestmobile0105/index.html&h=290&w=500&sz=19&hl=en&start=10&tbnid=QW_WUpg-Zf5p_M:&tbnh=75&tbnw=130&prev=/images%3Fq%3Dcellular%2Btelephones%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG


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2.1

Kms 0 km 100 km 150 km 200 km 250 km 300 km

Budget R295 R295 R295 R295 R295 R295

Avis R220 R220 R220 R220 R227,50 R370Value R245 R245 R245 R245 R297,50 R350

2.2

Comparison of car hire

0

50

100

150

200

250

300

350

400

0 km 100 km 150 km 200 km 250 km 300 km

No. of Kilometres

Costofcarhire

Budget

Avis

Value

2.3 Avis

2.4 Avis

2.5 Budget

http://images.google.co.za/imgres?imgurl=http://www.havanacarhire.com/images/gaviota-carhire-montage2.jpg&imgrefurl=http://www.drivecuba.com/&h=293&w=450&sz=47&hl=en&start=14&tbnid=kwrDHvKoQzXiiM:&tbnh=83&tbnw=127&prev=/images%3Fq%3Dcar%2Bhire%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG


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3.1.1 R3 000 x 80 = R240 000

3.1.2 R3 300 x 80 = R264 000

3.1.3 R3 712,50 x 80 = R297 000

3.1.4 R4 455 x 80 = R356 400

3.2.1 R3 000 x 190 = R570 000

3.2.2 R3 300 x 190 = R627 000

3.2.3 R3 712,50 x 190 = R705 375

3.2.4 R4 455 x 190 = R846 450

3.3

Comparison of the cost of building

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

80 90 100 110 120 130 140 150 160 170 180 190

Square metres

Costofbuilding

2004

2005

2006

2007

http://images.google.co.za/imgres?imgurl=http://www.coxesroost.net/journal/images/2005/11/08/houses.png&imgrefurl=http://www.coxesroost.net/journal/2005/11&h=300&w=300&sz=3&hl=en&start=7&tbnid=-igQyRWzQOC8sM:&tbnh=116&tbnw=116&prev=/images%3Fq%3Dhouses%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG


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3.4

Comparison of the cost of building

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

80 90 100 110 120 130 140 150 160 170 180 190

Square metres

Costofbuilding

2004

2005

2006

2007

The cost of building 120m house in 2007 is R534 600.

http://images.google.co.za/imgres?imgurl=http://pinker.wjh.harvard.edu/photos/Iceland/images/houses.jpg&imgrefurl=http://pinker.wjh.harvard.edu/photos/Iceland/pages/houses.htm&h=600&w=904&sz=104&hl=en&start=10&tbnid=fo4HWGI4XeZFCM:&tbnh=98&tbnw=147&prev=/images%3Fq%3Dhouses%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG

9 LO2 Multiple Graphs

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