Algebra, NAPX-p109130v01

Question

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Worked Solution

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Variant 0

DifficultyLevel

584

Question

A college marching band is made up of 102 people.

There are 24 more men than women.

How many women are there?

Worked Solution

Strategy 1

Check each option:

30+(30+24)=8430+(30+24)=84  x

39+(39+24)=10239+(39+24)=102  ✓\checkmark

∴\therefore There are 39 women.


Strategy 2

There are 24 more men than women.

Let  W\ W = number of women
W+(W+24)W+(W+24) = 102
2W2W = 78
∴W\therefore W = 39

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A college marching band is made up of 102 people. There are 24 more men than women. How many women are there?
workedSolution
Strategy 1 Check each option: $30+(30+24)=84$  x $39+(39+24)=102$  $\checkmark$ $\therefore$ There are 39 women.
Strategy 2 There are 24 more men than women. Let $\ W$ = number of women
| | | | ------------: | ---------- | | $W+(W+24)$ | \= 102 | | $2W$ | \= 78 | | $\therefore W$ | \= {{{correctAnswer}}} |
correctAnswer
39

Answers

Is Correct?Answer
x

30

✓

39

x

65

x

78

Variant 1

DifficultyLevel

596

Question

On a given day, the RSPCA had 87 lost dogs and cats in its care.

If there was 11 more dogs than cats, how many dogs were there?

Worked Solution

Strategy 1

Check each option:

38+(38 − 11)=6538+(38\ −\ 11)=65  x

49+(49 − 11)=8749+(49\ −\ 11)=87  ✓\checkmark

∴\therefore There are 49 dogs.


Strategy 2

There are 11 more dogs than cats.

Let  D\ D = number of dogs
D+(D − 11)D+(D\ − \ 11) = 87
2D2D = 98
∴D\therefore D = 49

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
On a given day, the RSPCA had 87 lost dogs and cats in its care. If there was 11 more dogs than cats, how many dogs were there?
workedSolution
Strategy 1 Check each option: $38+(38\ −\ 11)=65$  x $49+(49\ −\ 11)=87$  $\checkmark$ $\therefore$ There are 49 dogs.
Strategy 2 There are 11 more dogs than cats. Let $\ D$ = number of dogs
| | | | ------------: | ---------- | | $D+(D\ − \ 11)$ | \= 87 | | $2D$ | \= 98 | | $\therefore D$ | \= {{{correctAnswer}}} |
correctAnswer
49

Answers

Is Correct?Answer
x

38

✓

49

x

53

x

76

Variant 2

DifficultyLevel

584

Question

An AFL club has 68 junior players registered.

There are 10 more girls registered than boys.

How many boys are registered with the club?

Worked Solution

Strategy 1

By trial and error:

If number of boys = 29,

Total players
= 29 + 29 + 10
= 68  ✓\checkmark

Strategy 2

Let  n\ \large n = number of boys registered
n+n\large n + n + 10 = 68
2n\large n = 58
n\large n = 29

∴\therefore 29 boys are registered.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
An AFL club has 68 junior players registered. There are 10 more girls registered than boys. How many boys are registered with the club?
workedSolution
Strategy 1 By trial and error: If number of boys = 29, sm_nogap Total players
>| | | -------------------- | | = 29 + 29 + 10 | | = 68  $\checkmark$|

Strategy 2 sm_nogap Let $\ \large n$ = number of boys registered
| | | | --------------------: | -------------- | | $\large n + n$ + 10 | \= 68 | | 2$\large n$ | \= 58 | | $\large n$ | \= 29 |

$\therefore$ {{correctAnswer}} boys are registered.
correctAnswer
29

Answers

Is Correct?Answer
✓

29

x

30

x

44

x

60

Variant 3

DifficultyLevel

586

Question

At the fishing club weigh-in there were 45 fish weighed in.

There were 17 more flathead weighed in than bream.

How many bream were weighed in?

Worked Solution

Strategy 1

Check each option:
12 + 12 + 17 = 41  x
13 + 13 + 17 = 43  x
14 + 14 + 17 = 45  ✓\checkmark

Strategy 2

Let  n\ \large n = number of bream weighed in
n+n\large n + n + 17 = 45
2n\large n = 28
n\large n = 14

∴\therefore 14 bream are weighed in.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
At the fishing club weigh-in there were 45 fish weighed in. There were 17 more flathead weighed in than bream. How many bream were weighed in?
workedSolution
Strategy 1 sm_nogap Check each option:
>| | | -------------------- | | 12 + 12 + 17 = 41  x | | 13 + 13 + 17 = 43  x | | 14 + 14 + 17 = 45  $\checkmark$|

Strategy 2 sm_nogap Let $\ \large n$ = number of bream weighed in
| | | | --------------------: | -------------- | | $\large n + n$ + 17 | \= 45 | | 2$\large n$ | \= 28 | | $\large n$ | \= 14 |

$\therefore$ {{correctAnswer}} bream are weighed in.
correctAnswer
14

Answers

Is Correct?Answer
x

12

x

13

✓

14

x

28

Variant 4

DifficultyLevel

576

Question

In a fruit bowl containing apples and bananas, there are 37 pieces of fruit.

There are 5 more apples than bananas.

How many bananas are there?

Worked Solution

Strategy 1

Check each option:
42 + 42 + 5 = 89  x
32 + 32 + 5 = 69  x
16 + 16 + 5 = 37  ✓\checkmark

Strategy 2

Let  n\ \large n = number of bananas
n+n\large n + n + 5 = 37
2n\large n = 32
n\large n = 16

∴\therefore 16 bananas are in the fruit bowl.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
In a fruit bowl containing apples and bananas, there are 37 pieces of fruit. There are 5 more apples than bananas. How many bananas are there?
workedSolution
Strategy 1 sm_nogap Check each option:
>| | | -------------------- | | 42 + 42 + 5 = 89  x | | 32 + 32 + 5 = 69  x | | 16 + 16 + 5 = 37  $\checkmark$|

Strategy 2 sm_nogap Let $\ \large n$ = number of bananas
| | | | --------------------: | -------------- | | $\large n + n$ + 5 | \= 37 | | 2$\large n$ | \= 32 | | $\large n$ | \= 16 |

$\therefore$ {{correctAnswer}} bananas are in the fruit bowl.
correctAnswer
16

Answers

Is Correct?Answer
x

32

x

42

✓

16

x

15

Variant 5

DifficultyLevel

582

Question

A manufacturing plant has made 238 cars. All the cars are either hatch-backs or SUVs.

There are 74 more hatch-backs than SUVs.

How many hatch-backs are there?

Worked Solution

Strategy 1

Check each option:
82 + (82 − 74) = 90  x
156 + (156 − 74) = 238  ✓\checkmark

Strategy 2

Let  n\ \large n = number of hatch-backs
n\large n + (n\large n − 74) = 238
2n\large n = 312
n\large n = 156

∴\therefore 156 hatch-backs in the carpark.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A manufacturing plant has made 238 cars. All the cars are either hatch-backs or SUVs. There are 74 more hatch-backs than SUVs. How many hatch-backs are there?
workedSolution
Strategy 1 sm_nogap Check each option:
>| | | -------------------- | | 82 + (82 − 74) = 90  x | | 156 + (156 − 74) = 238  $\checkmark$|

Strategy 2 sm_nogap Let $\ \large n$ = number of hatch-backs
| | | | --------------------: | -------------- | | $\large n$ + ($\large n$ − 74) | \= 238 | | 2$\large n$ | \= 312 | | $\large n$ | \= 156 |

$\therefore$ {{correctAnswer}} hatch-backs in the carpark.
correctAnswer
156

Answers

Is Correct?Answer
x

82

✓

156

x

164

x

312

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