Number, NAPX-H3-NC32 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

733

Question

Tamaki owns a Japanese garden.

Her garden pond has twice as many carp as bream, and four times as many bream as frogs.

The pond has 24 more bream than frogs.

How many carp does Tamaki's garden pond have?

Worked Solution

Let  C\ C = number of carp

Let  B\ B = number of bream

Let  F\ F = number of frogs

Express the information in 3 equations:
CC = 2B ... (1)2B\ ... \ (1)
BB = 4F … (2)4F \ … \ (2)
24 = B−FB - F ...  (3)\ (3)

Substitute  B=4F\ B = 4F  into (3)
24 = 4F−F4F - F
3F3F = 24
FF = 8

Number of frogs = 8

Number of bream = 4×8=324 \times 8 =32
∴\therefore Number of carp = 2×322 \times 32
= 64

Question Type

Answer Box

Variables

Variable nameVariable value
question
Tamaki owns a Japanese garden. Her garden pond has twice as many carp as bream, and four times as many bream as frogs. The pond has 24 more bream than frogs. How many carp does Tamaki's garden pond have?
workedSolution
Let $\ C$ = number of carp Let $\ B$ = number of bream Let $\ F$ = number of frogs sm_nogap Express the information in 3 equations:
>| | | | ------------: | ---------- | | $C$ | \= $2B\ ... \ (1)$ | | $B$ | \= $4F \ … \ (2)$ | | 24 | \= $B - F$ ... $\ (3)$ |

sm_nogap Substitute $\ B = 4F$  into (3)
>| | | | -------------: | ---------- | | 24| \= $4F - F$ | | $3F$ | \= 24 | | $F$ | \= 8 |

Number of frogs = 8 sm_nogap Number of bream = $4 \times 8 =32$
| | | | -------------: | ---------- | | $\therefore$ Number of carp | \= $2 \times 32$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
64
prefix0
suffix0
carp

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
correctAnswer064

carp

Variant 1

DifficultyLevel

735

Question

Rosemary owns a fragrant garden.

Her fragrant garden has twice as many roses as lavender plants, and three times as many lavender plants as jasmine.

The garden has 60 more lavender plants than jasmine.

How many roses does Rosemary's fragrant garden have?

Worked Solution

Let  L\ L = number of lavender plants

Let  R\ R = number of roses

Let  J\ J = number of jasmine

Express the information in 3 equations:
RR = 2L ... (1)2L\ ... \ (1)
LL = 3J … (2)3J \ … \ (2)
60 = L−JL - J ...  (3)\ (3)

Substitute  L=3J\ L = 3J  into (3)
60 = 3J−J3J - J
2J2J = 60
JJ = 30

Number of jasmine = 30

Number of lavender = 3×30=903 \times 30 =90
∴\therefore Number of roses = 2×902 \times 90
= 180

Question Type

Answer Box

Variables

Variable nameVariable value
question
Rosemary owns a fragrant garden. Her fragrant garden has twice as many roses as lavender plants, and three times as many lavender plants as jasmine. The garden has 60 more lavender plants than jasmine. How many roses does Rosemary's fragrant garden have?
workedSolution
Let $\ L$ = number of lavender plants Let $\ R$ = number of roses Let $\ J$ = number of jasmine sm_nogap Express the information in 3 equations:
>| | | | ------------: | ---------- | | $R$ | \= $2L\ ... \ (1)$ | | $L$ | \= $3J \ … \ (2)$ | | 60 | \= $L - J$ ... $\ (3)$ |

sm_nogap Substitute $\ L = 3J$  into (3)
>| | | | -------------: | ---------- | | 60| \= $3J - J$ | | $2J$ | \= 60 | | $J$ | \= 30 |

Number of jasmine = 30 Number of lavender = $3 \times 30 =90$
| | | | ------------- | ---------- | | $\therefore$ Number of roses | \= $2 \times 90$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
180
prefix0
suffix0
roses

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
correctAnswer0180

roses

Variant 2

DifficultyLevel

737

Question

Gene has been shopping at the farmers' market to buy fruit.

He bought twice as many apples as pears, and 5 times as many pears as bananas.

He has 8 more pears than bananas.

How many apples did he buy?

Worked Solution

Let  A\ A = number of apples

Let  P\ P = number of pears

Let  B\ B = number of bananas

Express the information in 3 equations:
AA = 2P ... (1)2P\ ... \ (1)
PP = 5B … (2)5B \ … \ (2)
8 = P−BP - B ...  (3)\ (3)

Substitute  P=5B\ P = 5B  into (3)
8 = 5B−B5B - B
4B4B = 8
BB = 2

Number of bananas = 2

Number of pears = 5×2=105 \times 2 =10
∴\therefore Number of apples = 2×102 \times 10
= 20

Question Type

Answer Box

Variables

Variable nameVariable value
question
Gene has been shopping at the farmers' market to buy fruit. He bought twice as many apples as pears, and 5 times as many pears as bananas. He has 8 more pears than bananas. How many apples did he buy?
workedSolution
Let $\ A$ = number of apples Let $\ P$ = number of pears Let $\ B$ = number of bananas sm_nogap Express the information in 3 equations:
>| | | | ------------: | ---------- | | $A$ | \= $2P\ ... \ (1)$ | | $P$ | \= $5B \ … \ (2)$ | | 8 | \= $P - B$ ... $\ (3)$ |

sm_nogap Substitute $\ P = 5B$  into (3)
>| | | | -------------: | ---------- | | 8| \= $5B - B$ | | $4B$ | \= 8 | | $B$ | \= 2 |

Number of bananas = 2 Number of pears = $5 \times 2 =10$
| | | | ------------- | ---------- | | $\therefore$ Number of apples | \= $2 \times 10$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
20
prefix0
suffix0
apples

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
correctAnswer020

apples

Variant 3

DifficultyLevel

739

Question

Christian collects Formula One model racing cars.

His collection has three times as many Ferraris as McLarens, and two times as many McLarens as Alfa Romeos.

Christian's collection has 3 more McLarens than Alfa Romeos.

How many Formula One model racing cars are in Christian's collection?

Worked Solution

Let  F\ F = number of Ferraris

Let  M\ M = number of McLarens

Let  A\ A = number of Alfa Romeos

Express the information in 3 equations:
FF = 3M ... (1)3M\ ... \ (1)
MM = 2A … (2)2A \ … \ (2)
3 = M−AM - A ...  (3)\ (3)

Substitute  M=2A\ M = 2A  into (3)
3 = 2A−A2A - A
AA = 3

Number of Alfa Romeos = 3

Number of McLarens = 3×2=63 \times 2 = 6

Number of Ferraris = 3×6=183 \times 6 = 18
∴\therefore Total Formula One cars in collection = 3 + 6 + 18
= 27

Question Type

Answer Box

Variables

Variable nameVariable value
question
Christian collects Formula One model racing cars. His collection has three times as many Ferraris as McLarens, and two times as many McLarens as Alfa Romeos. Christian's collection has 3 more McLarens than Alfa Romeos. How many Formula One model racing cars are in Christian's collection?
workedSolution
Let $\ F$ = number of Ferraris Let $\ M$ = number of McLarens Let $\ A$ = number of Alfa Romeos sm_nogap Express the information in 3 equations:
>| | | | ------------: | ---------- | | $F$ | \= $3M\ ... \ (1)$ | | $M$ | \= $2A \ … \ (2)$ | | 3 | \= $M - A$ ... $\ (3)$ |

sm_nogap Substitute $\ M = 2A$  into (3)
>| | | | -------------: | ---------- | | 3| \= $2A - A$ | | $A$| \= 3 |

Number of Alfa Romeos = 3 Number of McLarens = $3 \times 2 = 6$ Number of Ferraris = $3 \times 6 = 18$
| | | | ------------- | ---------- | | $\therefore$ Total Formula One cars in collection | \= 3 + 6 + 18 | | | \= {{{correctAnswer0}}} |
correctAnswer0
27
prefix0
suffix0
Model Cars

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
correctAnswer027

Model Cars

Variant 4

DifficultyLevel

741

Question

A bag contains coloured marbles.

The bag has four times as many red marbles as blue marbles, and half as many blue marbles as green marbles.

The bag has 20 more green marbles than blue marbles.

How many marbles are in the bag?

Worked Solution

Let  R\ R = number of red marbles

Let  B\ B = number of blue marbles

Let  G\ G = number of green marbles

Express the information in 3 equations:
RR = 4B ... (1)4B\ ... \ (1)
BB = 12G… (2)\dfrac{1}{2}G … \ (2)
20 = G−BG - B ...  (3)\ (3)

Substitute  B\ B = 12G\dfrac{1}{2}G  into (3)
20 = G−12GG - \dfrac{1}{2}G
12G\dfrac{1}{2}G = 20
GG = 40

Number of green marbles = 40

Number of blue marbles = 12×40=20\dfrac{1}{2} \times 40 =20

Number of red marbles =  4×20=80\ 4 \times 20 =80
∴\therefore Total marbles in bag = 40+20+8040 + 20 + 80
= 140

Question Type

Answer Box

Variables

Variable nameVariable value
question
A bag contains coloured marbles. The bag has four times as many red marbles as blue marbles, and half as many blue marbles as green marbles. The bag has 20 more green marbles than blue marbles. How many marbles are in the bag?
workedSolution
Let $\ R$ = number of red marbles Let $\ B$ = number of blue marbles Let $\ G$ = number of green marbles sm_nogap Express the information in 3 equations:
>| | | | ------------: | ---------- | | $R$ | \= $4B\ ... \ (1)$ | | $B$ | \= $\dfrac{1}{2}G … \ (2)$ | | 20 | \= $G - B$ ... $\ (3)$ |

sm_nogap Substitute $\ B$ \= $\dfrac{1}{2}G$  into (3)
>| | | | -------------: | ---------- | | 20| \= $G - \dfrac{1}{2}G$ | | $\dfrac{1}{2}G$ | \= 20 | | $G$ | \= 40 |

Number of green marbles = 40 Number of blue marbles = $\dfrac{1}{2} \times 40 =20$ Number of red marbles = $\ 4 \times 20 =80$
| | | | ------------- | ---------- | | $\therefore$ Total marbles in bag | \= $40 + 20 + 80$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
140
prefix0
suffix0
red marbles

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
correctAnswer0140

red marbles

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