30244

Question

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Worked Solution

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Variant 0

DifficultyLevel

573

Question

A vegetable garden measures 2 metres by 1.5 metres.

Jim plants rows of lettuces in the garden, making sure there is a 20 cm gap between the garden edge and a plant, and 40 cm between each plant.


What is the maximum number of lettuces Jim can plant?

Worked Solution

Remove the 20 cm gaps from the garden edges:
Effective length = 200−20−20200 - 20 - 20 = 160 cm
Effective width = 150−20−20150 - 20 - 20 = 110 cm

Rows
16040=4⇒5 rows\dfrac{160}{40} = 4 \Rightarrow 5 \ \text{rows}

Columns
11040=2+⇒\dfrac{110}{40} = 2+ \Rightarrow 3 columns

Number of lettuces = 5 ×\times 3
= 15

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
part1
A vegetable garden measures 2 metres by 1.5 metres. Jim plants rows of lettuces in the garden, making sure there is a 20 cm gap between the garden edge and a plant, and 40 cm between each plant.
image1
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2021/03/RAPH-Q1_var0-1.svg 350 indent3 vpad
part2
sm_nogap What is the maximum number of lettuces Jim can plant?
solution1
sm_nogap Remove the 20 cm gaps from the garden edges:
| | | | ------- :| ----------------------------------- | | Effective length| = $200 - 20 - 20$ = 160 cm | | Effective width | = $150 - 20 - 20$ = 110 cm |
sm_nogap Rows
| | | ------------------------------------------------------------------ | | $\dfrac{160}{40} = 4 \Rightarrow 5 \ \text{rows}$ | sm_nogap Columns | | | ---------------------------------------------------------------------- | | $\dfrac{110}{40} = 2+ \Rightarrow$ 3 columns |

| | | | ------------------------------- | --------------- | | Number of lettuces | = 5 $\times$ 3 | | | = 15 |
correctAnswer
15

Answers

Is Correct?Answer
x

8

x

12

✓

15

x

20

Variant 1

DifficultyLevel

575

Question

A vegetable garden measures 3 metres by 1.5 metres.

Sinead plants rows of sweet potatoes in the garden, making sure there is a 30 cm gap between the garden edge and a plant, and 20 cm between each plant.


What is the maximum number of sweet potatoes that Sinead can plant?

Worked Solution

Remove the 30 cm gaps from the garden edges:
Effective length = 300−30−30300 - 30 - 30 = 240 cm
Effective width = 150−30−30150 - 30 - 30 = 90 cm

Rows
24020=12⇒13 rows\dfrac{240}{20} = 12 \Rightarrow 13 \ \text{rows}

Columns
9020=4.5⇒\dfrac{90}{20} = 4.5 \Rightarrow 5 columns

Number of sweet potatoes = 13 ×\times 5
= 65

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
part1
A vegetable garden measures 3 metres by 1.5 metres. Sinead plants rows of sweet potatoes in the garden, making sure there is a 30 cm gap between the garden edge and a plant, and 20 cm between each plant.
image1
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2021/03/RAPH-Q1_var1.svg 350 indent3 vpad
part2
What is the maximum number of sweet potatoes that Sinead can plant?
solution1
sm_nogap Remove the 30 cm gaps from the garden edges:
| | | | ------- :| ----------------------------------- | | Effective length| = $300 - 30 - 30$ = 240 cm | | Effective width | = $150 - 30 - 30$ = 90 cm |

sm_nogap Rows
| | | ------------------------------------------------------------------ | | $\dfrac{240}{20} = 12 \Rightarrow 13 \ \text{rows}$ | sm_nogap Columns | | | ---------------------------------------------------------------------- | | $\dfrac{90}{20} = 4.5 \Rightarrow$ 5 columns |

| | | | ------------------------------- | --------------- | | Number of sweet potatoes | = 13 $\times$ 5 | | | = 65 |
correctAnswer
65

Answers

Is Correct?Answer
x

30

x

48

x

54

✓

65

Variant 2

DifficultyLevel

573

Question

A vegetable garden measures 3 metres by 1 metres.

Marley plants rows of celeriac in the garden, making sure there is a 15 cm gap between the garden edge and a plant, and 30 cm between each plant.


What is the maximum number of celeriac plants that Marley can fit in the vegetable garden?

Worked Solution

Remove the 15 cm gaps from the garden edges:
Effective length = 300−15−15300 - 15 - 15 = 270 cm
Effective width = 100−15−15100 - 15 - 15 = 70 cm

Rows
27030=9⇒10 rows\dfrac{270}{30} = 9 \Rightarrow 10 \ \text{rows}

Columns
7030=2+⇒\dfrac{70}{30} = 2+ \Rightarrow 3 columns

Number of celeriac plants = 10 ×\times 3
= 30

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
part1
A vegetable garden measures 3 metres by 1 metres. Marley plants rows of celeriac in the garden, making sure there is a 15 cm gap between the garden edge and a plant, and 30 cm between each plant.
image1
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2021/03/RAPH-Q1_var2.svg 350 indent3 vpad
part2
What is the maximum number of celeriac plants that Marley can fit in the vegetable garden?
solution1
sm_nogap Remove the 15 cm gaps from the garden edges:
| | | | ------- :| ----------------------------------- | | Effective length| = $300 - 15 - 15$ = 270 cm | | Effective width | = $100 - 15 - 15$ = 70 cm |

sm_nogap Rows
| | | ------------------------------------------------------------------ | | $\dfrac{270}{30} = 9 \Rightarrow 10 \ \text{rows}$ | sm_nogap Columns | | | ---------------------------------------------------------------------- | | $\dfrac{70}{30} = 2+ \Rightarrow$ 3 columns |

| | | | ------------------------------- | --------------- | | Number of celeriac plants | = 10 $\times$ 3 | | | = 30 |
correctAnswer
30

Answers

Is Correct?Answer
x

15

x

20

x

27

✓

30

Variant 3

DifficultyLevel

573

Question

A vegetable garden measures 2 metres by 1.5 metres.

Bjork plants rows of beetroot in the garden, making sure there is a 10 cm gap between the garden edge and a plant, and 30 cm between each plant.


What is the maximum number of beetroot plants that Bjork can plant?

Worked Solution

Remove the 10 cm gaps from the garden edges:
Effective length = 200−10−10200 - 10 - 10 = 180 cm
Effective width = 150−10−10150 - 10 - 10 = 130 cm

Rows
18030=6⇒7 rows\dfrac{180}{30} = 6 \Rightarrow 7 \ \text{rows}

Columns
13030=4+⇒\dfrac{130}{30} = 4+ \Rightarrow 5 columns

Number of beetroot plants = 7 ×\times 5
= 35

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
part1
A vegetable garden measures 2 metres by 1.5 metres. Bjork plants rows of beetroot in the garden, making sure there is a 10 cm gap between the garden edge and a plant, and 30 cm between each plant.
image1
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2021/03/RAPH-Q1_var3.svg 350 indent3 vpad
part2
What is the maximum number of beetroot plants that Bjork can plant?
solution1
sm_nogap Remove the 10 cm gaps from the garden edges:
| | | | ------- :| ----------------------------------- | | Effective length| = $200 - 10 - 10$ = 180 cm | | Effective width | = $150 - 10 - 10$ = 130 cm |

sm_nogap Rows
| | | ------------------------------------------------------------------ | | $\dfrac{180}{30} = 6 \Rightarrow 7 \ \text{rows}$ | sm_nogap Columns | | | ---------------------------------------------------------------------- | | $\dfrac{130}{30} = 4+ \Rightarrow$ 5 columns |

| | | | ------------------------------- | --------------- | | Number of beetroot plants | = 7 $\times$ 5 | | | = 35 |
correctAnswer
35

Answers

Is Correct?Answer
x

20

x

24

x

30

✓

35

Variant 4

DifficultyLevel

576

Question

A vegetable garden measures 3 metres by 1 metre.

Beau plants rows of garlic in the garden, making sure there is a 15 cm gap between the garden edge and a plant, and 20 cm between each plant.


What is the maximum number of garlic plants that Beau can fit in the vegetable garden?

Worked Solution

Remove the 15 cm gaps from the garden edges:
Effective length = 300−15−15300 - 15 - 15 = 270 cm
Effective width = 100−15−15100 - 15 - 15 = 70 cm

Rows
27020=13.5⇒14 rows\dfrac{270}{20} = 13.5 \Rightarrow 14 \ \text{rows}

Columns
7020=3.5⇒\dfrac{70}{20} = 3.5 \Rightarrow 4 columns

Number of garlic plants = 14 ×\times 4
= 56

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
part1
A vegetable garden measures 3 metres by 1 metre. Beau plants rows of garlic in the garden, making sure there is a 15 cm gap between the garden edge and a plant, and 20 cm between each plant.
image1
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2021/03/RAPH-Q1_var4.svg 350 indent3 vpad
part2
What is the maximum number of garlic plants that Beau can fit in the vegetable garden?
solution1
sm_nogap Remove the 15 cm gaps from the garden edges:
| | | | ------- :| ----------------------------------- | | Effective length| = $300 - 15 - 15$ = 270 cm | | Effective width | = $100 - 15 - 15$ = 70 cm |

sm_nogap Rows
| | | ------------------------------------------------------------------ | | $\dfrac{270}{20} = 13.5 \Rightarrow 14 \ \text{rows}$ | sm_nogap Columns | | | ---------------------------------------------------------------------- | | $\dfrac{70}{20} = 3.5 \Rightarrow$ 4 columns |

| | | | ------------------------------- | --------------- | | Number of garlic plants | = 14 $\times$ 4 | | | = 56 |
correctAnswer
56

Answers

Is Correct?Answer
x

39

x

52

✓

56

x

60