Algebra, NAPX-J4-CA29 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

628

Question

Indigo is a lawyer who charges $250 to look at a case and then a fixed price for each minute she spends on the case.

The graph below shows Indigo's charge based on the number of minutes she spends on the case.



How much will Indigo charge for a case that takes 60 minutes of her time?

Worked Solution

Initial charge = $250

From the graph,

⇒ 50 minute case costs $400

Cost per minute =400−25050\dfrac{400 - 250}{50} = $3

∴\therefore Cost of 60 minute case

=250+60×3=250+60×3

= $430

Question Type

Answer Box

Variables

Variable nameVariable value
question
Indigo is a lawyer who charges $250 to look at a case and then a fixed price for each minute she spends on the case. The graph below shows Indigo's charge based on the number of minutes she spends on the case.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-J4-CA29-SA_v0_1.svg 300 indent vpad
How much will Indigo charge for a case that takes 60 minutes of her time?
workedSolution
Initial charge = $250 From the graph, ⇒ 50 minute case costs $400 Cost per minute =$\dfrac{400 - 250}{50}$ = $3 sm_nogap $\therefore$ Cost of 60 minute case >> $=250+60×3$ >> = {{{prefix0}}}{{{correctAnswer0}}}
correctAnswer0
430
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0430

$

Variant 1

DifficultyLevel

628

Question

Brendon is a lawyer who charges $150 to look at a case and then a fixed price for each minute he spends on the case.

The graph below shows Brendon's charge based on the number of minutes he spends on the case.



How much will Brendon charge for a case that takes 70 minutes of his time?

Worked Solution

Initial charge = $150

From the graph,

⇒ 50 minute case costs $300

Cost per minute =300−15050\dfrac{300 - 150}{50} = $3

∴\therefore Cost of 70 minute case

=150+70×3=150+70×3

= $360

Question Type

Answer Box

Variables

Variable nameVariable value
question
Brendon is a lawyer who charges $150 to look at a case and then a fixed price for each minute he spends on the case. The graph below shows Brendon's charge based on the number of minutes he spends on the case.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-J4-CA29-SA_v1_1.svg 320 indent vpad
How much will Brendon charge for a case that takes 70 minutes of his time?
workedSolution
Initial charge = $150 From the graph, ⇒ 50 minute case costs $300 Cost per minute =$\dfrac{300 - 150}{50}$ = $3 sm_nogap $\therefore$ Cost of 70 minute case >> $=150+70×3$ >> = {{{prefix0}}}{{{correctAnswer0}}}
correctAnswer0
360
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0360

$

Variant 2

DifficultyLevel

628

Question

Tahlia is a paralegal who charges $50 to look at a case and then a fixed price for each minute she spends on the case.

The graph below shows Tahlia's charge based on the number of minutes she spends on the case.


How much will Tahlia charge for a case that takes 80 minutes of her time?

Worked Solution

Initial charge = $50

From the graph,

⇒ 50 minute case costs $300


Cost per minute =300−5050\dfrac{300 - 50}{50} = $5

∴\therefore Cost of 80 minute case

=50+80×5=50+80×5

= $450

Question Type

Answer Box

Variables

Variable nameVariable value
question
Tahlia is a paralegal who charges $50 to look at a case and then a fixed price for each minute she spends on the case. The graph below shows Tahlia's charge based on the number of minutes she spends on the case. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-J4-CA29-SA_v2_2.svg 280 indent vpad
How much will Tahlia charge for a case that takes 80 minutes of her time?
workedSolution
Initial charge = $50 From the graph, ⇒ 50 minute case costs $300
Cost per minute =$\dfrac{300 - 50}{50}$ = $5 sm_nogap $\therefore$ Cost of 80 minute case >> $=50+80×5$ >> = {{{prefix0}}}{{{correctAnswer0}}}
correctAnswer0
450
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0450

$

Variant 3

DifficultyLevel

628

Question

Geordie wants to hire a stand-up paddle board. The hire company charges an hourly rate plus a flat fee of $25 for insurance.

The graph below shows the cost of board hire based on the number of hours the board is hired.



How much will Geordie pay for a stand-up paddle board hire of 5 hours?

Worked Solution

Initial fee = $25

From the graph,

⇒ 1 hour hire costs $40

Cost per hour = 40 −- 25 = $15

∴\therefore Cost of 5 hour hire

=25+15×5=25+15×5

= $100

Question Type

Answer Box

Variables

Variable nameVariable value
question
Geordie wants to hire a stand-up paddle board. The hire company charges an hourly rate plus a flat fee of $25 for insurance. The graph below shows the cost of board hire based on the number of hours the board is hired.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-J4-CA29-SA_v3_1.svg 350 indent vpad
How much will Geordie pay for a stand-up paddle board hire of 5 hours?
workedSolution
Initial fee = $25 From the graph, ⇒ 1 hour hire costs $40 Cost per hour = 40 $-$ 25 = $15 sm_nogap $\therefore$ Cost of 5 hour hire >> $=25+15×5$ >> = {{{prefix0}}}{{{correctAnswer0}}}
correctAnswer0
100
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0100

$

Variant 4

DifficultyLevel

630

Question

MaxiCab taxis charge a hire fee of $4 plus a charge per kilometre travelled.

The graph below shows the total charge of a ride based on the number of kilometres travelled.



How much will Preshan pay if she hires a MaxiCab to take her a distance of 35 kilometres from the airport to her home?

Worked Solution

Hire fee = $4

From the graph,

⇒ 10 kilometre trip costs $24

Cost per kilometre =24−410\dfrac{24 - 4}{10} = $2

∴\therefore Cost of 35 kilometre trip

=4+35×2=4+35×2

= $74

Question Type

Answer Box

Variables

Variable nameVariable value
question
MaxiCab taxis charge a hire fee of $4 plus a charge per kilometre travelled. The graph below shows the total charge of a ride based on the number of kilometres travelled.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-J4-CA29-SA_v4_1.svg 320 indent vpad
How much will Preshan pay if she hires a MaxiCab to take her a distance of 35 kilometres from the airport to her home?
workedSolution
Hire fee = $4 From the graph, ⇒ 10 kilometre trip costs $24 Cost per kilometre =$\dfrac{24 - 4}{10}$ = $2 sm_nogap $\therefore$ Cost of 35 kilometre trip >> $=4+35×2$ >> = {{{prefix0}}}{{{correctAnswer0}}}
correctAnswer0
74
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer074

$

Variant 5

DifficultyLevel

630

Question

Mavis' Hire Cars charge a hire fee of $6 plus a charge per kilometre travelled.

The graph below shows the total charge of a ride based on the number of kilometres travelled.



How much will Mahlia be charged if she rents a car and returns it after travelling 30 kilometres?

Worked Solution

Initial charge = $6

From the graph,

⇒ 20 kilometre trip costs $36

Cost per kilometre =36−620\dfrac{36 - 6}{20} = $1.50

∴\therefore Cost of 30 kilometre trip

=6+30×1.50=6+30×1.50

= $51

Question Type

Answer Box

Variables

Variable nameVariable value
question
Mavis' Hire Cars charge a hire fee of $6 plus a charge per kilometre travelled. The graph below shows the total charge of a ride based on the number of kilometres travelled.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-J4-CA29-SA_v5_1.svg 340 indent vpad
How much will Mahlia be charged if she rents a car and returns it after travelling 30 kilometres?
workedSolution
Initial charge = $6 From the graph, ⇒ 20 kilometre trip costs $36 Cost per kilometre =$\dfrac{36 - 6}{20}$ = $1.50 sm_nogap $\therefore$ Cost of 30 kilometre trip >> $=6+30×1.50$ >> = {{{prefix0}}}{{{correctAnswer0}}}
correctAnswer0
51
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer051

$

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