Number_gap-2026_707

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

705

Question

At a school fete there were 80 students and 120 adults.

45% of the students and 30% of the adults bought a raffle ticket.

What percentage of the whole group bought a raffle ticket?

Worked Solution
Students who bought a ticket = 45% ×\times 80
= 45100\dfrac{45}{100} ×\times 80
= 920\dfrac{9}{20} ×\times 80
= 9 ×\times 4 = 36

Adults who bought a ticket = 30% ×\times 120
= 30100\dfrac{30}{100} ×\times 120
= 310\dfrac{3}{10} ×\times 120
= 3 ×\times 12 = 36

Total who bought a ticket = 36 + 36 = 72
Total in group = 80 + 120 = 200
Percentage = 72200\dfrac{72}{200} ×\times 100
= 36100\dfrac{36}{100} ×\times 100
= 36%

Question Type

Answer Box

Variables

Variable nameVariable value
question
At a school fete there were 80 students and 120 adults. 45% of the students and 30% of the adults bought a raffle ticket. What percentage of the whole group bought a raffle ticket?
workedSolution
| | | | ------------------------------:| -------------------------------------------- | | Students who bought a ticket | \= 45% $\times$ 80 | | | \= $\dfrac{45}{100}$ $\times$ 80 | | | \= $\dfrac{9}{20}$ $\times$ 80 | | | \= 9 $\times$ 4 = 36 |

| | | | ------------------------------:| -------------------------------------------- | | Adults who bought a ticket | \= 30% $\times$ 120 | | | \= $\dfrac{30}{100}$ $\times$ 120 | | | \= $\dfrac{3}{10}$ $\times$ 120 | | | \= 3 $\times$ 12 = 36 |

| | | | ------------------------------:| -------------------------------------------- | | Total who bought a ticket | \= 36 + 36 = 72 | | Total in group | \= 80 + 120 = 200 | | Percentage | \= $\dfrac{72}{200}$ $\times$ 100 | | | \= $\dfrac{36}{100}$ $\times$ 100 | | | \= {{{correctAnswer0}}}%|
correctAnswer0
36
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
correctAnswer036

%

Variant 1

DifficultyLevel

708

Question

At a community event there were 80 adults and 120 children.

35% of the adults and 55% of the children enjoyed the event.

What percentage of the whole group enjoyed the event?

Worked Solution
Adults who enjoyed the event = 35% ×\times 80
= 35100\dfrac{35}{100} ×\times 80
= 720\dfrac{7}{20} ×\times 80
= 7 ×\times 4 = 28

Children who enjoyed the event = 55% ×\times 120
= 55100\dfrac{55}{100} ×\times 120
= 1120\dfrac{11}{20} ×\times 120
= 11 ×\times 6 = 66

Total who enjoyed the event = 28 + 66 = 94
Total in group = 80 + 120 = 200
Percentage = 94200\dfrac{94}{200} ×\times 100
= 47100\dfrac{47}{100} ×\times 100
= 47%

Question Type

Answer Box

Variables

Variable nameVariable value
question
At a community event there were 80 adults and 120 children. 35% of the adults and 55% of the children enjoyed the event. What percentage of the whole group enjoyed the event?
workedSolution
| | | | ------------------------------:| -------------------------------------------- | | Adults who enjoyed the event | \= 35% $\times$ 80 | | | \= $\dfrac{35}{100}$ $\times$ 80 | | | \= $\dfrac{7}{20}$ $\times$ 80 | | | \= 7 $\times$ 4 = 28 |

| | | | ------------------------------:| -------------------------------------------- | | Children who enjoyed the event | \= 55% $\times$ 120 | | | \= $\dfrac{55}{100}$ $\times$ 120 | | | \= $\dfrac{11}{20}$ $\times$ 120 | | | \= 11 $\times$ 6 = 66 |

| | | | ------------------------------:| -------------------------------------------- | | Total who enjoyed the event | \= 28 + 66 = 94 | | Total in group | \= 80 + 120 = 200 | | Percentage | \= $\dfrac{94}{200}$ $\times$ 100 | | | \= $\dfrac{47}{100}$ $\times$ 100 | | | \= {{{correctAnswer0}}}% |
correctAnswer0
47
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
correctAnswer047

%

Variant 2

DifficultyLevel

711

Question

In a survey, 150 men and 100 women were asked if they exercise daily.

30% of the men and 45% of the women said they exercise daily.

What percentage of the whole group exercises daily?

Worked Solution
Men who exercise daily = 30% ×\times 150
= 30100\dfrac{30}{100} ×\times 150
= 310\dfrac{3}{10} ×\times 150
= 3 ×\times 15 = 45

Women who exercise daily = 45% ×\times 100
= 45100\dfrac{45}{100} ×\times 100
= 45

Total who exercise daily = 45 + 45 = 90
Total in group = 150 + 100 = 250
Percentage = 90250\dfrac{90}{250} ×\times 100
= 925\dfrac{9}{25} ×\times 100
= 9 ×\times 4
= 36%

Question Type

Answer Box

Variables

Variable nameVariable value
question
In a survey, 150 men and 100 women were asked if they exercise daily. 30% of the men and 45% of the women said they exercise daily. What percentage of the whole group exercises daily?
workedSolution
| | | | ------------------------------:| -------------------------------------------- | | Men who exercise daily | \= 30% $\times$ 150 | | | \= $\dfrac{30}{100}$ $\times$ 150 | | | \= $\dfrac{3}{10}$ $\times$ 150 | | | \= 3 $\times$ 15 = 45 |

| | | | ------------------------------:| -------------------------------------------- | | Women who exercise daily | \= 45% $\times$ 100 | | | \= $\dfrac{45}{100}$ $\times$ 100 | | | \= 45 |

| | | | ------------------------------:| -------------------------------------------- | | Total who exercise daily | \= 45 + 45 = 90 | | Total in group | \= 150 + 100 = 250 | | Percentage | \= $\dfrac{90}{250}$ $\times$ 100 | | | \= $\dfrac{9}{25}$ $\times$ 100 | | | \= 9 $\times$ 4 | | | \= {{{correctAnswer0}}}% |
correctAnswer0
36
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
correctAnswer036

%

Variant 3

DifficultyLevel

713

Question

At a school, 120 students and 80 teachers were surveyed about whether they use public transport.

75% of the students and 25% of the teachers use public transport.

What percentage of the whole group uses public transport?

Worked Solution
Students who use public transport = 75% ×\times 120
= 75100\dfrac{75}{100} ×\times 120
= 34\dfrac{3}{4} ×\times 120
= 3 ×\times 30 = 90

Teachers who use public transport = 25% ×\times 80
= 25100\dfrac{25}{100} ×\times 80
= 14\dfrac{1}{4} ×\times 80
= 20

Total who use public transport = 90 + 20 = 110
Total in group = 120 + 80 = 200
Percentage = 110200\dfrac{110}{200} ×\times 100
= 1120\dfrac{11}{20} ×\times 100
= 11 ×\times 5
= 55%

Question Type

Answer Box

Variables

Variable nameVariable value
question
At a school, 120 students and 80 teachers were surveyed about whether they use public transport. 75% of the students and 25% of the teachers use public transport. What percentage of the whole group uses public transport?
workedSolution
| | | | ------------------------------:| -------------------------------------------- | | Students who use public transport | \= 75% $\times$ 120 | | | \= $\dfrac{75}{100}$ $\times$ 120 | | | \= $\dfrac{3}{4}$ $\times$ 120 | | | \= 3 $\times$ 30 = 90 |

| | | | ------------------------------:| -------------------------------------------- | | Teachers who use public transport | \= 25% $\times$ 80 | | | \= $\dfrac{25}{100}$ $\times$ 80 | | | \= $\dfrac{1}{4}$ $\times$ 80 | | | \= 20 |

| | | | ------------------------------:| -------------------------------------------- | | Total who use public transport | \= 90 + 20 = 110 | | Total in group | \= 120 + 80 = 200 | | Percentage | \= $\dfrac{110}{200}$ $\times$ 100 | | | \= $\dfrac{11}{20}$ $\times$ 100 | | | \= 11 $\times$ 5 | | | \= {{{correctAnswer0}}}% |
correctAnswer0
55
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
correctAnswer055

%

Variant 4

DifficultyLevel

715

Question

At a community club, 180 members and 120 non-members were asked if they voted yes in a recent poll.

55% of members and 40% of non-members voted yes.

What percentage of the whole group voted yes?

Worked Solution
Members who voted yes = 55% ×\times 180
= 55100\dfrac{55}{100} ×\times 180
= 1120\dfrac{11}{20} ×\times 180
= 11 ×\times 9 = 99

Non-members who voted yes = 40% ×\times 120
= 40100\dfrac{40}{100} ×\times 120
= 25\dfrac{2}{5} ×\times 120
= 2 ×\times 24 = 48

Total who voted yes = 99 + 48 = 147
Total in group = 180 + 120 = 300
Percentage = 147300\dfrac{147}{300} ×\times 100
= 49100\dfrac{49}{100} ×\times 100
= 49%

Question Type

Answer Box

Variables

Variable nameVariable value
question
At a community club, 180 members and 120 non-members were asked if they voted yes in a recent poll. 55% of members and 40% of non-members voted yes. What percentage of the whole group voted yes?
workedSolution
| | | | ------------------------------:| -------------------------------------------- | | Members who voted yes | \= 55% $\times$ 180 | | | \= $\dfrac{55}{100}$ $\times$ 180 | | | \= $\dfrac{11}{20}$ $\times$ 180 | | | \= 11 $\times$ 9 = 99 |

| | | | ------------------------------:| -------------------------------------------- | | Non-members who voted yes | \= 40% $\times$ 120 | | | \= $\dfrac{40}{100}$ $\times$ 120 | | | \= $\dfrac{2}{5}$ $\times$ 120 | | | \= 2 $\times$ 24 = 48 |

| | | | ------------------------------:| -------------------------------------------- | | Total who voted yes | \= 99 + 48 = 147 | | Total in group | \= 180 + 120 = 300 | | Percentage | \= $\dfrac{147}{300}$ $\times$ 100 | | | \= $\dfrac{49}{100}$ $\times$ 100 | | | \= {{{correctAnswer0}}}% |
correctAnswer0
49
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
correctAnswer049

%

Tags

  • staging_suejones