Number, NAPX9-TLF-CA38 SA v3

Question

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Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

701

Question

A dog breeder records the number of puppies born in litters to four of her dogs.

She also records the percentage of puppies in each litter that were sick.


Dogs Number of puppies Percentage sick
1 12 25%
2 4 50%
3 5 20%
4 4 50%

What percentage of the total number of puppies were sick?

Worked Solution

Total sick puppies
= 12 × 0.25 + 4 × 0.5 + 5 × 0.2 + 4 × 0.5
= 3 + 2 + 1 + 2
= 8

∴\therefore Percentage of sick puppies
= number of sick puppiestotal puppies×100\dfrac{\text{number of sick puppies}}{\text{total puppies}} \times 100
= 8(12+4+5+4)×100\dfrac{8}{(12 + 4 + 5 + 4)} \times 100
= 825×100\dfrac{8}{25} \times 100
= 32%

Question Type

Answer Box

Variables

Variable nameVariable value
question
A dog breeder records the number of puppies born in litters to four of her dogs. She also records the percentage of puppies in each litter that were sick.
>>| Dogs | Number of puppies | Percentage sick | |:-:|:-:|:-:| | 1 | 12| 25%| | 2 | 4| 50%| | 3 | 5| 20%| | 4 | 4| 50%|

What percentage of the total number of puppies were sick?
workedSolution
sm_nogap Total sick puppies
>>|| |-| |= 12 × 0.25 + 4 × 0.5 + 5 × 0.2 + 4 × 0.5| |= 3 + 2 + 1 + 2| |= 8|
sm_nogap $\therefore$ Percentage of sick puppies
>>|| |-| |= $\dfrac{\text{number of sick puppies}}{\text{total puppies}} \times 100$| ||| |= $\dfrac{8}{(12 + 4 + 5 + 4)} \times 100$| ||| |= $\dfrac{8}{25} \times 100$| |= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
32
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
correctAnswer032

%

Variant 1

DifficultyLevel

705

Question

A dog breeder records the number of puppies born in litters to four of her dogs.

She also records the percentage of puppies in each litter that were sick.


Dogs Number of puppies Percentage sick
1 12 25%
2 4 50%
3 5 20%
4 4 50%

What percentage of the total number of puppies were NOT sick?

Worked Solution

Total puppies
= 12 + 4 + 5 + 4
= 25

Total sick puppies
= 12 × 0.25 + 4 × 0.5 + 5 × 0.2 + 4 × 0.5
= 3 + 2 + 1 + 2
= 8

∴\therefore Number of puppies NOT sick
= 25 −- 8
= 17

∴\therefore Percentage of puppies NOT sick
= number of puppies NOT sicktotal puppies×100\dfrac{\text{number of puppies NOT sick}}{\text{total puppies}} \times 100
= 1725×100\dfrac{17}{25} \times 100
= 68%

Question Type

Answer Box

Variables

Variable nameVariable value
question
A dog breeder records the number of puppies born in litters to four of her dogs. She also records the percentage of puppies in each litter that were sick.
>>| Dogs | Number of puppies | Percentage sick | |:-:|:-:|:-:| | 1 | 12| 25%| | 2 | 4| 50%| | 3 | 5| 20%| | 4 | 4| 50%|

What percentage of the total number of puppies were NOT sick?
workedSolution
sm_nogap Total puppies
>>|| |-| |= 12 + 4 + 5 + 4| |= 25|
sm_nogap Total sick puppies
>>|| |-| |= 12 × 0.25 + 4 × 0.5 + 5 × 0.2 + 4 × 0.5| |= 3 + 2 + 1 + 2| |= 8|
sm_nogap $\therefore$ Number of puppies NOT sick
>>|| |-| |= 25 $-$ 8| |= 17|
sm_nogap $\therefore$ Percentage of puppies NOT sick
>>|| |-| |= $\dfrac{\text{number of puppies NOT sick}}{\text{total puppies}} \times 100$| ||| |= $\dfrac{17}{25} \times 100$| ||| |= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
68
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
correctAnswer068

%

Variant 2

DifficultyLevel

697

Question

A farmer records the number of eggs laid by 4 chickens in his coup in a week.

He also records the percentage of eggs laid that were fertilised.


Chicken Eggs laid Percentage fertilised
1 5 20%
2 6 50%
3 4 75%
4 10 30%

What percentage of the total number of eggs were fertilised?

Worked Solution

Total eggs
= 5 + 6 + 4 + 10
= 25

Total eggs fertilised
= 5 × 0.2 + 6 × 0.5 + 4 × 0.75 + 10 × 0.3
= 1 + 3 + 3 + 3
= 10

∴\therefore Percentage of eggs fertilised
= eggs fertilisedtotal eggs×100\dfrac{\text{eggs fertilised}}{\text{total eggs}} \times 100
= 1025×100\dfrac{10}{25} \times 100
= 40%

Question Type

Answer Box

Variables

Variable nameVariable value
question
A farmer records the number of eggs laid by 4 chickens in his coup in a week. He also records the percentage of eggs laid that were fertilised.
>>| Chicken | Eggs laid | Percentage fertilised | |:-:|:-:|:-:| | 1 | 5| 20%| | 2 | 6| 50%| | 3 | 4| 75%| | 4 | 10| 30%|

What percentage of the total number of eggs were fertilised?
workedSolution
sm_nogap Total eggs
>>|| |-| |= 5 + 6 + 4 + 10| |= 25|
sm_nogap Total eggs fertilised
>>|| |-| |= 5 × 0.2 + 6 × 0.5 + 4 × 0.75 + 10 × 0.3| |= 1 + 3 + 3 + 3| |= 10|
sm_nogap $\therefore$ Percentage of eggs fertilised
>>|| |-| |= $\dfrac{\text{eggs fertilised}}{\text{total eggs}} \times 100$| ||| |= $\dfrac{10}{25} \times 100$| ||| |= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
40
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
correctAnswer040

%

Variant 3

DifficultyLevel

690

Question

Three Ridgeback dog breeders record the number of Ridgeback puppies they sell in a month.

The breeders also record the percentage of the puppies sold that are liver-nosed.


Breeder Ridgeback puppies sold Percentage liver-nosed
1 8 75%
2 2 50%
3 15 60%

What percentage of the total number of puppies sold were liver-nosed?

Worked Solution

Total Ridgeback puppies
= 8 + 2 + 15
= 25

Total liver-nosed puppies
= 8 × 0.75 + 2 × 0.5 + 15 × 0.6
= 6 + 1 + 9
= 16

∴\therefore Percentage of liver-nosed
= total liver-nosedtotal puppies×100\dfrac{\text{total liver-nosed}}{\text{total puppies}} \times 100
= 1625×100\dfrac{16}{25} \times 100
= 64%

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three Ridgeback dog breeders record the number of Ridgeback puppies they sell in a month. The breeders also record the percentage of the puppies sold that are liver-nosed.
>>| Breeder | Ridgeback puppies sold | Percentage liver-nosed | |:-:|:-:|:-:| | 1 | 8| 75%| | 2 | 2| 50%| | 3 | 15| 60%|

What percentage of the total number of puppies sold were liver-nosed?
workedSolution
sm_nogap Total Ridgeback puppies
>>|| |-| |= 8 + 2 + 15| |= 25|
sm_nogap Total liver-nosed puppies
>>|| |-| |= 8 × 0.75 + 2 × 0.5 + 15 × 0.6| |= 6 + 1 + 9| |= 16|
sm_nogap $\therefore$ Percentage of liver-nosed
>>|| |-| |= $\dfrac{\text{total liver-nosed}}{\text{total puppies}} \times 100$| ||| |= $\dfrac{16}{25} \times 100$| ||| |= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
64
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
correctAnswer064

%

Variant 4

DifficultyLevel

692

Question

A researcher records the number of koalas she tags in three expeditions.

She also records the percentage of tagged koalas that were female.


Expedition Koalas tagged Percentage female
1 8 25%
2 2 50%
3 10 40%

What percentage of the total number of tagged koalas were female?

Worked Solution

Total koalas
= 8 + 2 + 10
= 20

Total female koalas
= 8 × 0.25 + 2 × 0.5 + 10 × 0.4
= 2 + 1 + 4
= 7

∴\therefore Percentage of females
= total femalestotal koalas×100\dfrac{\text{total females}}{\text{total koalas}} \times 100
= 720×100\dfrac{7}{20} \times 100
= 35%

Question Type

Answer Box

Variables

Variable nameVariable value
question
A researcher records the number of koalas she tags in three expeditions. She also records the percentage of tagged koalas that were female.
>>| Expedition | Koalas tagged | Percentage female | |:-:|:-:|:-:| | 1 | 8| 25%| | 2 | 2| 50%| | 3 | 10| 40%|

What percentage of the total number of tagged koalas were female?
workedSolution
sm_nogap Total koalas
>>|| |-| |= 8 + 2 + 10| |= 20|
sm_nogap Total female koalas
>>|| |-| |= 8 × 0.25 + 2 × 0.5 + 10 × 0.4| |= 2 + 1 + 4| |= 7|
sm_nogap $\therefore$ Percentage of females
>>|| |-| |= $\dfrac{\text{total females}}{\text{total koalas}} \times 100$| ||| |= $\dfrac{7}{20} \times 100$| ||| |= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
35
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
correctAnswer035

%

Variant 5

DifficultyLevel

694

Question

A researcher records the number of elephants in the largest 3 zoos in his country.

He also records the percentage of the elephants in each zoo that were African.


Zoo Number of elephants Percentage of African elephants
1 12 25%
2 4 75%
3 4 50%

What percentage of the total number of elephants are African?

Worked Solution

Total elephants
= 12 + 4 + 4
= 20

Total African elephants
= 12 × 0.25 + 4 × 0.75 + 4 × 0.5
= 3 + 3 + 2
= 8

∴\therefore Percentage of African elephants
= total African elphantstotal elephants×100\dfrac{\text{total African elphants}}{\text{total elephants}} \times 100
= 820×100\dfrac{8}{20} \times 100
= 40%

Question Type

Answer Box

Variables

Variable nameVariable value
question
A researcher records the number of elephants in the largest 3 zoos in his country. He also records the percentage of the elephants in each zoo that were African.
>>| Zoo | Number of elephants | Percentage of African elephants | |:-:|:-:|:-:| | 1 | 12| 25%| | 2 | 4| 75%| | 3 | 4| 50%|

What percentage of the total number of elephants are African?
workedSolution
sm_nogap Total elephants
>>|| |-| |= 12 + 4 + 4| |= 20|
sm_nogap Total African elephants
>>|| |-| |= 12 × 0.25 + 4 × 0.75 + 4 × 0.5| |= 3 + 3 + 2| |= 8|
sm_nogap $\therefore$ Percentage of African elephants
>>|| |-| |= $\dfrac{\text{total African elphants}}{\text{total elephants}} \times 100$| ||| |= $\dfrac{8}{20} \times 100$| ||| |= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
40
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
correctAnswer040

%

Tags

  • ms_ca