50170

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

588

Question

There are 74 year 7 students enrolled at a school.

There are 12 more girls enrolled than boys.

How many boys are enrolled in year 7?

Worked Solution

Strategy 1

By trial and error using given options:

30+(30+12)=7230 + (30 + 12) = 72  x

31+(31+12)=7431 + (31 + 12) = 74  ✓\checkmark

∴\therefore There are 31 boys enrolled.


Strategy 2

Let  n\large n = number of boys enrolled

⇒n\Rightarrow \large n + 12 = number of girls enrolled
n+n\large n + n + 12 = 74
2n2\large n = 62
n\large n = 31

∴\therefore There are 31 boys enrolled.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
There are 74 year 7 students enrolled at a school. There are 12 more girls enrolled than boys. How many boys are enrolled in year 7?
workedSolution
Strategy 1 By trial and error using given options: $30 + (30 + 12) = 72$  x $31 + (31 + 12) = 74$  $\checkmark$ $\therefore$ There are {{correctAnswer}} boys enrolled.
Strategy 2
Let  $\large n$ = number of boys enrolled
$\Rightarrow \large n$ + 12 = number of girls enrolled
| | | | --------------------: | -------------- | | $\large n + n$ + 12 | \= 74 | | $2\large n$ | \= 62 | | $\large n$ | \= {{correctAnswer}} | $\therefore$ There are {{correctAnswer}} boys enrolled.
correctAnswer
31

Answers

Is Correct?Answer
x

30

✓

31

x

43

x

62

Variant 1

DifficultyLevel

590

Question

There are 190 year 9 students enrolled at a school.

There are 16 more boys enrolled than girls.

How many girls are enrolled in year 9?

Worked Solution

Strategy 1

By trial and error using given options:

87+(87+16)=19087 + (87 + 16) = 190  ✓\checkmark

∴\therefore There are 87 girls enrolled.


Strategy 2

Let  n\large n = number of girls enrolled

⇒n\Rightarrow \large n + 16 = number of boys enrolled
n+n\large n + n + 16 = 190
2n2\large n = 174
n\large n = 87

∴\therefore There are 87 girls enrolled.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
There are 190 year 9 students enrolled at a school. There are 16 more boys enrolled than girls. How many girls are enrolled in year 9?
workedSolution
Strategy 1 By trial and error using given options: $87 + (87 + 16) = 190$  $\checkmark$ $\therefore$ There are {{correctAnswer}} girls enrolled.
Strategy 2
Let  $\large n$ = number of girls enrolled
$\Rightarrow \large n$ + 16 = number of boys enrolled
| | | | --------------------: | -------------- | | $\large n + n$ + 16 | \= 190 | | $2\large n$ | \= 174 | | $\large n$ | \= {{correctAnswer}} | $\therefore$ There are {{correctAnswer}} girls enrolled.
correctAnswer
87

Answers

Is Correct?Answer
✓

87

x

88

x

103

x

174

Variant 2

DifficultyLevel

592

Question

A junior soccer club has 315 registered players.

There are 51 less boys registered than girls.

How many of the registered players are girls?

Worked Solution

Strategy 1

By trial and error using given options:

132+(132132 + (132 −- 51)=21351) = 213  x

180+(180180 + (180 −- 51)=30951) = 309  x

183+(183183 + (183 −- 51)=31551) = 315  ✓\checkmark

∴\therefore There are 183 girls registered.


Strategy 2

Let  n\large n = number of girls registered

⇒n\Rightarrow \large n −- 51 = number of boys registered
n+n\large n + n −- 51 = 315
2n2\large n = 315 + 51
2n2\large n = 366
n\large n = 183

∴\therefore There are 183 girls registered.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A junior soccer club has 315 registered players. There are 51 less boys registered than girls. How many of the registered players are girls?
workedSolution
Strategy 1 By trial and error using given options: $132 + (132$ $-$ $51) = 213$  x $180 + (180$ $-$ $51) = 309$  x $183 + (183$ $-$ $51) = 315$  $\checkmark$ $\therefore$ There are {{correctAnswer}} girls registered.
Strategy 2
Let  $\large n$ = number of girls registered
$\Rightarrow \large n$ $-$ 51 = number of boys registered
| | | | --------------------: | -------------- | | $\large n + n$ $-$ 51 | \= 315 | | $2\large n$ | \= 315 + 51 | | $2\large n$ | \= 366 | | $\large n$ | \= {{correctAnswer}} | $\therefore$ There are {{correctAnswer}} girls registered.
correctAnswer
183

Answers

Is Correct?Answer
x

132

x

180

✓

183

x

264

Variant 3

DifficultyLevel

594

Question

An over 18's concert was attended by 7000 people over the three day event.

There were 5200 more people in the age group 30 or under than the over 30 age group.

How many of the concert goers were over the age of 30?

Worked Solution

Strategy 1

By trial and error using given options:

900+(900+5200)=7000900 + (900 + 5200) = 7000  ✓\checkmark

∴\therefore There are 900 at concert older than 30.


Strategy 2

Let  n\large n = number at concert older than 30

⇒n\Rightarrow \large n + 5200 = number at concert 30 or under
n+n\large n + n + 5200 = 7000
2n2\large n = 7000 −- 5200
2n2\large n = 1800
n\large n = 900

∴\therefore There are 900 at concert older than 30.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
An over 18's concert was attended by 7000 people over the three day event. There were 5200 more people in the age group 30 or under than the over 30 age group. How many of the concert goers were over the age of 30?
workedSolution
Strategy 1 By trial and error using given options: $900 + (900 + 5200) = 7000$  $\checkmark$ $\therefore$ There are {{correctAnswer}} at concert older than 30.
Strategy 2
Let  $\large n$ = number at concert older than 30
$\Rightarrow \large n$ + 5200 = number at concert 30 or under
| | | | --------------------: | -------------- | | $\large n + n$ + 5200 | \= 7000 | | $2\large n$ | \= 7000 $-$ 5200 | | $2\large n$ | \= 1800 | | $\large n$ | \= {{correctAnswer}} | $\therefore$ There are {{correctAnswer}} at concert older than 30.
correctAnswer
900

Answers

Is Correct?Answer
✓

900

x

1800

x

3300

x

6100

Variant 4

DifficultyLevel

596

Question

A rose farm produced a total of 1500 red and white long stemmed roses for Valentine's Day.

There are 600 less white roses picked than red.

How many of the roses picked are red?

Worked Solution

Strategy 1

By trial and error using given options:

150+(150150 + (150 −- 600)=−300600) = − 300  x

750+(750750 + (750 −- 600)=900600) = 900  x

1050+(10501050 + (1050 −- 600)=1500600) = 1500  ✓\checkmark

∴\therefore There are 1050 red roses.


Strategy 2

Let  n\large n = number of red roses

⇒n\Rightarrow \large n −- 600 = number of white roses
n+n\large n + n −- 600 = 1500
2n2\large n = 1500 + 600
2n2\large n = 2100
n\large n = 1050

∴\therefore There are 1050 red roses.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A rose farm produced a total of 1500 red and white long stemmed roses for Valentine's Day. There are 600 less white roses picked than red. How many of the roses picked are red?
workedSolution
Strategy 1 By trial and error using given options: $150 + (150$ $-$ $600) = − 300$  x $750 + (750$ $-$ $600) = 900$  x $1050 + (1050$ $-$ $600) = 1500$  $\checkmark$ $\therefore$ There are {{correctAnswer}} red roses.
Strategy 2
Let  $\large n$ = number of red roses
$\Rightarrow \large n$ $-$ 600 = number of white roses
| | | | --------------------: | -------------- | | $\large n + n$ $-$ 600 | \= 1500 | | $2\large n$ | \= 1500 + 600 | | $2\large n$ | \= 2100 | | $\large n$ | \= {{correctAnswer}} | $\therefore$ There are {{correctAnswer}} red roses.
correctAnswer
1050

Answers

Is Correct?Answer
x

150

x

750

✓

1050

x

2100

Variant 5

DifficultyLevel

589

Question

There are 156 birds in an aviary.

All the birds are either canaries or finches and there are 82 more finches than canaries.

How many canaries are in the aviary?

Worked Solution

Strategy 1

By trial and error using given options:

34+(34+82)=15034 + (34 + 82) = 150  x

37+(37+82)=15637 + (37 + 82) = 156  ✓\checkmark

∴\therefore There are 37 canaries in the aviary.


Strategy 2

Let  n\large n = number of canaries in the aviary

⇒n\Rightarrow \large n + 82 = number of finches in the aviary
n+n\large n + n + 82 = 156
2n2\large n = 156 −- 82
2n2\large n = 74
n\large n = 37

∴\therefore There are 37 canaries in the aviary.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
There are 156 birds in an aviary. All the birds are either canaries or finches and there are 82 more finches than canaries. How many canaries are in the aviary?
workedSolution
Strategy 1 By trial and error using given options: $34 + (34 + 82) = 150$  x $37 + (37 + 82) = 156$  $\checkmark$ $\therefore$ There are {{correctAnswer}} canaries in the aviary.
Strategy 2
Let  $\large n$ = number of canaries in the aviary
$\Rightarrow \large n$ + 82 = number of finches in the aviary
| | | | --------------------: | -------------- | | $\large n + n$ + 82 | \= 156 | | $2\large n$ | \= 156 $-$ 82 | | $2\large n$ | \= 74 | | $\large n$ | \= {{correctAnswer}} | $\therefore$ There are {{correctAnswer}} canaries in the aviary.
correctAnswer
37

Answers

Is Correct?Answer
x

34

✓

37

x

78

x

119

Tags