Algebra, NAP_30301

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

546

Question

Reba is taking part in a push-up challenge that lasts for 7 days.

On the first day he completes 22 push-ups. Every day after this he intends to increase the number of push-ups he does by 8.

How many push-ups will Reba do on the last day of the challenge?

Worked Solution

Strategy 1:

Consider the push-ups Reba completes each day

Number of push-ups Day 1 = 22

Number of push-ups Day 2 = 22 + 8 = 30

Number of push-ups Day 3 = 30 + 8 = 38

Number of push-ups Day 4 = 38 + 8 = 46

Number of push-ups Day 5 = 46 + 8 = 54

Number of push-ups Day 6 = 54 + 8 = 62

Number of push-ups Day 7 = 62 + 8 = 70


Therefore, Reba completed 70 push-ups on the seventh day.

Strategy 2: (Advanced)
Push-ups = 22 + 8 ×\times (day number - 1)
= 22 + 8 ×\times (7 −- 1)
= 22 + 8 ×\times 6
= 70

Therefore, Reba completed 70 push-ups on the seventh day.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Reba is taking part in a push-up challenge that lasts for 7 days. On the first day he completes 22 push-ups. Every day after this he intends to increase the number of push-ups he does by 8. How many push-ups will Reba do on the last day of the challenge?
workedSolution
Strategy 1: Consider the push-ups Reba completes each day >Number of push-ups Day 1 = 22 >Number of push-ups Day 2 = 22 + 8 = 30 >Number of push-ups Day 3 = 30 + 8 = 38 >Number of push-ups Day 4 = 38 + 8 = 46 >Number of push-ups Day 5 = 46 + 8 = 54 >Number of push-ups Day 6 = 54 + 8 = 62 >Number of push-ups Day 7 = 62 + 8 = {{{correctAnswer}}}
Therefore, Reba completed {{{correctAnswer}}} push-ups on the seventh day. Strategy 2: (Advanced)
| | | | ------------- | ---------- | | Push-ups | = 22 + 8 $\times$ (day number - 1) | | | = 22 + 8 $\times$ (7 $-$ 1) | | | = 22 + 8 $\times$ 6 | | | \= {{{correctAnswer}}} |

Therefore, Reba completed {{{correctAnswer}}} push-ups on the seventh day.
correctAnswer
70

Answers

Is Correct?Answer
x

78

✓

70

x

56

x

48

Variant 1

DifficultyLevel

548

Question

Huxley is taking part in a running challenge that lasts for 8 weeks.

During the first week he runs a total of 30 kilometres. Every week after that he intends to increase the number of kilometres he runs by 4.

How many kilometres will Huxley run on the last day of the challenge?

Worked Solution

Strategy 1:

Consider the kilometres Huxley completes each week

Number of kilometres week 1 = 30

Number of kilometres week 2 = 30 + 4 = 34

Number of kilometres week 3 = 34 + 4 = 38

Number of kilometres week 4 = 38 + 4 = 42

Number of kilometres week 5 = 42 + 4 = 46

Number of kilometres week 6 = 46 + 4 = 50

Number of kilometres week 7 = 50 + 4 = 54

Number of kilometres week 8 = 54 + 4 = 58


Therefore, Huxley completed 58 kilometres during the 8th week.

Strategy 2: (Advanced)
Kilometres = 30 + 4 ×\times (week number - 1)
= 30 + 4 ×\times (8 −- 1)
= 30 + 4 ×\times 7
= 58

Therefore, Huxley completed 58 kilometres during the 8th week.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Huxley is taking part in a running challenge that lasts for 8 weeks. During the first week he runs a total of 30 kilometres. Every week after that he intends to increase the number of kilometres he runs by 4. How many kilometres will Huxley run on the last day of the challenge?
workedSolution
Strategy 1: Consider the kilometres Huxley completes each week >Number of kilometres week 1 = 30 >Number of kilometres week 2 = 30 + 4 = 34 >Number of kilometres week 3 = 34 + 4 = 38 >Number of kilometres week 4 = 38 + 4 = 42 >Number of kilometres week 5 = 42 + 4 = 46 >Number of kilometres week 6 = 46 + 4 = 50 >Number of kilometres week 7 = 50 + 4 = 54 >Number of kilometres week 8 = 54 + 4 = {{{correctAnswer}}}
Therefore, Huxley completed {{{correctAnswer}}} kilometres during the 8th week. Strategy 2: (Advanced)
| | | | ------------- | ---------- | | Kilometres | = 30 + 4 $\times$ (week number - 1) | | | = 30 + 4 $\times$ (8 $-$ 1) | | | = 30 + 4 $\times$ 7 | | | \= {{{correctAnswer}}} |

Therefore, Huxley completed {{{correctAnswer}}} kilometres during the 8th week.
correctAnswer
58

Answers

Is Correct?Answer
x

48

x

54

✓

58

x

62

Variant 2

DifficultyLevel

550

Question

Burt is saving to go on a holiday in 6 months time.

He already has $470 saved and intends to add a futher $140 each month for the next 6 months.

How much money will Burt have saved, in total, by the time he goes on holidays?

Worked Solution

Strategy 1:

Consider the amount Burt saves each month

Amount already saved = $470

Amount saved after 1 month = 470 + 140 = 610

Amount saved after 2 months = 610 + 140 = 750

Amount saved after 3 months = 750 + 140 = 890

Amount saved after 4 months = 890 + 140 = 1030

Amount saved after 5 months = 1030 + 140 = 1170

Amount saved after 6 months = 1170 + 140 = $1310


Therefore, Burt has saved $1310 for his holiday.

Strategy 2: (Advanced)
Savings = 470 + 140 ×\times month number
= 470 + 140 ×\times 6
= 470 + 840
= $1310

Therefore, Burt has saved $1310 for his holiday.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Burt is saving to go on a holiday in 6 months time. He already has $470 saved and intends to add a futher $140 each month for the next 6 months. How much money will Burt have saved, in total, by the time he goes on holidays?
workedSolution
Strategy 1: Consider the amount Burt saves each month >Amount already saved = $470 >Amount saved after 1 month = 470 + 140 = 610 >Amount saved after 2 months = 610 + 140 = 750 >Amount saved after 3 months = 750 + 140 = 890 >Amount saved after 4 months = 890 + 140 = 1030 >Amount saved after 5 months = 1030 + 140 = 1170 >Amount saved after 6 months = 1170 + 140 = {{{correctAnswer}}}
Therefore, Burt has saved {{{correctAnswer}}} for his holiday. Strategy 2: (Advanced)
| | | | ------------- | ---------- | | Savings | = 470 + 140 $\times$ month number | | | = 470 + 140 $\times$ 6 | | | = 470 + 840 | | | \= {{{correctAnswer}}} |

Therefore, Burt has saved {{{correctAnswer}}} for his holiday.
correctAnswer
$1310

Answers

Is Correct?Answer
x

$1450

✓

$1310

x

$1170

x

$840

Variant 3

DifficultyLevel

552

Question

Betty is taking part in a walking challenge that lasts for 5 weeks.

During the first week she walks 37 kilometres. Every week after this she intends to increase the number of kilometres she walks by 3.

How many kilometres will Betty walk during the last week of the challenge?

Worked Solution

Strategy 1:

Consider the kilometres Betty walks each week

Number of kilometres week 1 = 37

Number of kilometres week 2 = 37 + 3 = 40

Number of kilometres week 3 = 40 + 3 = 43

Number of kilometres week 4 = 43 + 3 = 46

Number of kilometres week 5 = 46 + 3 = 49


Therefore, Betty walked 49 kilometres during the 5th week.

Strategy 2: (Advanced)
Kilometres = 37 + 3 ×\times (week number - 1)
= 37 + 3 ×\times (5 −- 1)
= 37 + 3 ×\times 4
= 49

Therefore, Betty walked 49 kilometres during the 5th week.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Betty is taking part in a walking challenge that lasts for 5 weeks. During the first week she walks 37 kilometres. Every week after this she intends to increase the number of kilometres she walks by 3. How many kilometres will Betty walk during the last week of the challenge?
workedSolution
Strategy 1: Consider the kilometres Betty walks each week >Number of kilometres week 1 = 37 >Number of kilometres week 2 = 37 + 3 = 40 >Number of kilometres week 3 = 40 + 3 = 43 >Number of kilometres week 4 = 43 + 3 = 46 >Number of kilometres week 5 = 46 + 3 = {{{correctAnswer}}}
Therefore, Betty walked {{{correctAnswer}}} kilometres during the 5th week. Strategy 2: (Advanced)
| | | | ------------- | ---------- | | Kilometres | = 37 + 3 $\times$ (week number - 1) | | | = 37 + 3 $\times$ (5 $-$ 1) | | | = 37 + 3 $\times$ 4 | | | \= {{{correctAnswer}}} |

Therefore, Betty walked {{{correctAnswer}}} kilometres during the 5th week.
correctAnswer
49

Answers

Is Correct?Answer
✓

49

x

52

x

57

x

111

Variant 4

DifficultyLevel

554

Question

George is taking part in a 100 metre sprinting challenge and he records his best 100 metre time each week for 6 weeks.

During the first week he records a best time of 31 seconds. Every week after this he intends to reduce his weekly best time by 2 seconds.

What should George's best time be during the last week of the challenge if he has achieved his goal?

Worked Solution

Strategy 1:

Consider the times George records each week

Best time week 1 = 31

Best time week 2 = 31 −- 2 = 29

Best time week 3 = 29 −- 2 = 27

Best time week 4 = 27 −- 2 = 25

Best time week 5 = 25 −- 2 = 23

Best time week 6 = 23 −- 2 = 21


Therefore, George records a best time of 21 seconds during the 6th week of the Challenge.

Strategy 2: (Advanced)
Push-ups = 31 −- 2 ×\times (week number - 1)
= 31 −- 2 ×\times (6 −- 1)
= 31 −- 2 ×\times 5
= 21

Therefore, George records a best time of 21 seconds during the 6th week of the Challenge.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
George is taking part in a 100 metre sprinting challenge and he records his best 100 metre time each week for 6 weeks. During the first week he records a best time of 31 seconds. Every week after this he intends to reduce his weekly best time by 2 seconds. What should George's best time be during the last week of the challenge if he has achieved his goal?
workedSolution
Strategy 1: Consider the times George records each week >Best time week 1 = 31 >Best time week 2 = 31 $-$ 2 = 29 >Best time week 3 = 29 $-$ 2 = 27 >Best time week 4 = 27 $-$ 2 = 25 >Best time week 5 = 25 $-$ 2 = 23 >Best time week 6 = 23 $-$ 2 = {{{correctAnswer}}}
Therefore, George records a best time of {{{correctAnswer}}} seconds during the 6th week of the Challenge. Strategy 2: (Advanced)
| | | | ------------- | ---------- | | Push-ups | = 31 $-$ 2 $\times$ (week number - 1) | | | = 31 $-$ 2 $\times$ (6 $-$ 1) | | | = 31 $-$ 2 $\times$ 5 | | | \= {{{correctAnswer}}} |

Therefore, George records a best time of {{{correctAnswer}}} seconds during the 6th week of the Challenge.
correctAnswer
21

Answers

Is Correct?Answer
x

41

x

25

x

23

✓

21

Tags

  • staging_suejones