9 lo2 multiple graphs
TRANSCRIPT
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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.
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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.
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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?
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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.
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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
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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.
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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
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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
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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.
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