Algebra, NAPX-G4-CA30

Question

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Worked Solution

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Variant 0

DifficultyLevel

731

Question

Bellarose collects insects.

14\dfrac{1}{4} of her collection are beetles and 16\dfrac{1}{6} of her collection are bees.

Bellarose has 6 more beetles than bees in her collection.

How many insects are in Bellarose's collection in total?

Worked Solution

Solution 1

Let  x\ \large x = total number of insects
14x\dfrac{1}{4}\large x −- 16x\dfrac{1}{6}\large x = 6
312x\dfrac{3}{12}\large x −- 212x\dfrac{2}{12}\large x = 6
112x\dfrac{1}{12}\large x = 6
x\large x = 72

Solution 2

By trial and error:

14×72=18\dfrac{1}{4} \times 72=18 beetles

16×72=12\dfrac{1}{6} \times 72=12 bees

beetles −- bees = 18 −- 12 = 6

∴\therefore 72 insects in total.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Bellarose collects insects. $\dfrac{1}{4}$ of her collection are beetles and $\dfrac{1}{6}$ of her collection are bees. Bellarose has 6 more beetles than bees in her collection. How many insects are in Bellarose's collection in total?
workedSolution
Solution 1 sm_nogap Let $\ \large x$ = total number of insects
| | | | ------------: | ---------- | | $\dfrac{1}{4}\large x$ $-$ $\dfrac{1}{6}\large x$ | \= 6 | | $\dfrac{3}{12}\large x$ $-$ $\dfrac{2}{12}\large x$ | \= 6 | | $\dfrac{1}{12}\large x$ | \= 6 | | $\large x$| \= {{{correctAnswer}}} |

Solution 2 By trial and error: $\dfrac{1}{4} \times 72=18$ beetles $\dfrac{1}{6} \times 72=12$ bees beetles $-$ bees = 18 $-$ 12 = 6 $\therefore$ {{{correctAnswer}}} insects in total.
correctAnswer
72

Answers

Is Correct?Answer
x

24

x

36

x

60

✓

72

Variant 1

DifficultyLevel

738

Question

Edgell grows vegetables in a market garden.

15\dfrac{1}{5} of his crop are carrots and 14\dfrac{1}{4} of his crop are potatoes.

Edgell has 95 more potato plants than carrots in his market garden.

How many plants are in Edgell's market garden in total?

Worked Solution

Solution 1

Let  x\ \large x = total number of plants
14x\dfrac{1}{4}\large x −- 15x\dfrac{1}{5}\large x = 95
520x\dfrac{5}{20}\large x −- 420x\dfrac{4}{20}\large x = 95
120x\dfrac{1}{20}\large x = 95
x\large x = 1900

Solution 2

By trial and error:

14×1900=475\dfrac{1}{4} \times 1900=475 potatoes

15×1900=380\dfrac{1}{5} \times 1900=380 carrots

potatoes −- carrots = 475 −- 380 = 95

∴\therefore 1900 plants in total.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Edgell grows vegetables in a market garden. $\dfrac{1}{5}$ of his crop are carrots and $\dfrac{1}{4}$ of his crop are potatoes. Edgell has 95 more potato plants than carrots in his market garden. How many plants are in Edgell's market garden in total?
workedSolution
Solution 1 sm_nogap Let $\ \large x$ = total number of plants
| | | | ------------: | ---------- | | $\dfrac{1}{4}\large x$ $-$ $\dfrac{1}{5}\large x$ | \= 95 | | $\dfrac{5}{20}\large x$ $-$ $\dfrac{4}{20}\large x$ | \= 95 | | $\dfrac{1}{20}\large x$ | \= 95 | | $\large x$| \= {{{correctAnswer}}} |

Solution 2 By trial and error: $\dfrac{1}{4} \times 1900=475$ potatoes $\dfrac{1}{5} \times 1900=380$ carrots potatoes $-$ carrots = 475 $-$ 380 = 95 $\therefore$ {{{correctAnswer}}} plants in total.
correctAnswer
1900

Answers

Is Correct?Answer
✓

1900

x

855

x

211

x

43

Variant 2

DifficultyLevel

735

Question

Sage collects sea shells on the beach.

12\dfrac{1}{2} of her collection are scallop shells and 13\dfrac{1}{3} of her collection are cowrie shells.

Sage has 16 more scallop shells than cowrie shells in her collection.

How many sea shells are in Sage's collection in total?

Worked Solution

Solution 1

Let  x\ \large x = total number of sea shells
12x\dfrac{1}{2}\large x −- 13x\dfrac{1}{3}\large x = 16
36x\dfrac{3}{6}\large x −- 26x\dfrac{2}{6}\large x = 16
16x\dfrac{1}{6}\large x = 16
x\large x = 96

Solution 2

By trial and error:

12×96=48\dfrac{1}{2} \times 96=48 scallop shells

13×96=32\dfrac{1}{3} \times 96=32 cowrie shells

scallop shells −- cowrie shells = 48 −- 32 = 16

∴\therefore 96 sea shells in total.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Sage collects sea shells on the beach. $\dfrac{1}{2}$ of her collection are scallop shells and $\dfrac{1}{3}$ of her collection are cowrie shells. Sage has 16 more scallop shells than cowrie shells in her collection. How many sea shells are in Sage's collection in total?
workedSolution
Solution 1 sm_nogap Let $\ \large x$ = total number of sea shells
| | | | ------------: | ---------- | | $\dfrac{1}{2}\large x$ $-$ $\dfrac{1}{3}\large x$ | \= 16 | | $\dfrac{3}{6}\large x$ $-$ $\dfrac{2}{6}\large x$ | \= 16 | | $\dfrac{1}{6}\large x$ | \= 16 | | $\large x$| \= {{{correctAnswer}}} |

Solution 2 By trial and error: $\dfrac{1}{2} \times 96=48$ scallop shells $\dfrac{1}{3} \times 96=32$ cowrie shells scallop shells $-$ cowrie shells = 48 $-$ 32 = 16 $\therefore$ {{{correctAnswer}}} sea shells in total.
correctAnswer
96

Answers

Is Correct?Answer
x

112

✓

96

x

80

x

29

Variant 3

DifficultyLevel

739

Question

Sydney writes backing music for advertisements.

35\dfrac{3}{5} of the money he has earned came from music he wrote in 2019 and 12\dfrac{1}{2} of the money he has earned came from music he wrote in 2020.

Sydney earned $24 000 more in 2019 than in 2020.

How much money has Sydney earned in total?

Worked Solution

Solution 1

Let  x\ \large x = total amount earned
35x\dfrac{3}{5}\large x −- 12x\dfrac{1}{2}\large x = $24 000
610x\dfrac{6}{10}\large x −- 510x\dfrac{5}{10}\large x = $24 000
110x\dfrac{1}{10}\large x = $24 000
x\large x = $240 000

Solution 2

By trial and error:

35×240 000=144 000\dfrac{3}{5} \times 240\ 000=144 \ 000

12×240 000=120 000\dfrac{1}{2} \times 240\ 000 = 120 \ 000

2019 earnings −- 2020 earnings = 144 000 − 120 000 = $24 000

∴\therefore $240 000 earnings in total.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Sydney writes backing music for advertisements. $\dfrac{3}{5}$ of the money he has earned came from music he wrote in 2019 and $\dfrac{1}{2}$ of the money he has earned came from music he wrote in 2020. Sydney earned $24 000 more in 2019 than in 2020. How much money has Sydney earned in total?
workedSolution
Solution 1 sm_nogap Let $\ \large x$ = total amount earned
| | | | ------------: | ---------- | | $\dfrac{3}{5}\large x$ $-$ $\dfrac{1}{2}\large x$ | \= $24 000 | | $\dfrac{6}{10}\large x$ $-$ $\dfrac{5}{10}\large x$ | \= $24 000 | | $\dfrac{1}{10}\large x$ | \= $24 000 | | $\large x$| \= {{{correctAnswer}}} |

Solution 2 By trial and error: $\dfrac{3}{5} \times 240\ 000=144 \ 000$ $\dfrac{1}{2} \times 240\ 000 = 120 \ 000$ 2019 earnings $-$ 2020 earnings = 144 000 − 120 000 = $24 000 $\therefore$ {{{correctAnswer}}} earnings in total.
correctAnswer
$240 000

Answers

Is Correct?Answer
x

$120 000

x

$144 000

✓

$240 000

x

$264 000

Variant 4

DifficultyLevel

731

Question

A bag contains coloured discs.

23\dfrac{2}{3} of the discs are purple and 16\dfrac{1}{6} of the discs are orange.

The bag has 18 more purple discs than orange discs.

How many discs are in the bag in total?

Worked Solution

Solution 1

Let  x\ \large x = total number of discs
23x\dfrac{2}{3}\large x −- 16x\dfrac{1}{6}\large x = 18
46x\dfrac{4}{6}\large x −- 16x\dfrac{1}{6}\large x = 18
12x\dfrac{1}{2}\large x = 18
x\large x = 36

Solution 2

By trial and error:

23×36=24\dfrac{2}{3} \times 36=24 purple discs

16×36=6\dfrac{1}{6} \times 36=6 orange discs

purple −- orange = 24 −- 6 = 18

∴\therefore 36 discs in total.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A bag contains coloured discs. $\dfrac{2}{3}$ of the discs are purple and $\dfrac{1}{6}$ of the discs are orange. The bag has 18 more purple discs than orange discs. How many discs are in the bag in total?
workedSolution
Solution 1 sm_nogap Let $\ \large x$ = total number of discs
| | | | ------------: | ---------- | | $\dfrac{2}{3}\large x$ $-$ $\dfrac{1}{6}\large x$ | \= 18 | | $\dfrac{4}{6}\large x$ $-$ $\dfrac{1}{6}\large x$ | \= 18 | | $\dfrac{1}{2}\large x$ | \= 18 | | $\large x$| \= {{{correctAnswer}}} |

Solution 2 By trial and error: $\dfrac{2}{3} \times 36=24$ purple discs $\dfrac{1}{6} \times 36=6$ orange discs purple $-$ orange = 24 $-$ 6 = 18 $\therefore$ {{{correctAnswer}}} discs in total.
correctAnswer
36

Answers

Is Correct?Answer
x

108

x

76

✓

36

x

27

Variant 5

DifficultyLevel

739

Question

iWatch streams a selection of movies, series and documentaries.

35\dfrac{3}{5} of the shows are movies and 320\dfrac{3}{20} of the shows are documentaries.

iWatch is currently streaming 36 more movies than documentaries.

How many shows are being streamed in total?

Worked Solution

Solution 1

Let  x\ \large x = total number of shows being streamed
35x\dfrac{3}{5}\large x −- 320x\dfrac{3}{20}\large x = 36
1220x\dfrac{12}{20}\large x −- 320x\dfrac{3}{20}\large x = 36
920x\dfrac{9}{20}\large x = 36
x\large x = 209×36\dfrac{20}{9} \times 36
x\large x = 80

Solution 2

By trial and error:

35×80=48\dfrac{3}{5} \times 80=48 movies

320×80=12\dfrac{3}{20} \times 80=12 documentaries

movies −- documentaries = 48 −- 12 = 36

∴\therefore 80 shows in total.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
iWatch streams a selection of movies, series and documentaries. $\dfrac{3}{5}$ of the shows are movies and $\dfrac{3}{20}$ of the shows are documentaries. iWatch is currently streaming 36 more movies than documentaries. How many shows are being streamed in total?
workedSolution
Solution 1 sm_nogap Let $\ \large x$ = total number of shows being streamed
| | | | ------------: | ---------- | | $\dfrac{3}{5}\large x$ $-$ $\dfrac{3}{20}\large x$ | \= 36 | | $\dfrac{12}{20}\large x$ $-$ $\dfrac{3}{20}\large x$ | \= 36 | | $\dfrac{9}{20}\large x$ | \= 36 | | $\large x$ | \= $\dfrac{20}{9} \times 36$ | | $\large x$| \= {{{correctAnswer}}} |

Solution 2 By trial and error: $\dfrac{3}{5} \times 80=48$ movies $\dfrac{3}{20} \times 80=12$ documentaries movies $-$ documentaries = 48 $-$ 12 = 36 $\therefore$ {{{correctAnswer}}} shows in total.
correctAnswer
80

Answers

Is Correct?Answer
x

12

x

44

x

48

✓

80

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