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Number and Algebra, NAP-J2-38

Karen stands on a box and her new height is 1.8 metres.

Karen's actual height is twice that of the box.

What is the height of the box in centimetres?

   centimetres
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`text(60 cm)`

Show Worked Solution
`text(1.8 metres)` `= 180\ text(centimetres)`
`180 ÷ 3` `= 60\ text(cm)`

 
`:.\ text(The height of the box is 60 cm.)`

Number and Algebra, NAP-K2-24

A volleyball club receives 16 boxes containing 32 club jerseys each.

It then gives 8 jerseys to every team in the club and there are no jerseys left over.

How many teams are in the club?

`16` `48` `56` `64`
 
 
 
 
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`21`

Show Worked Solution

`text(Strategy 1:)`

`text{1 box → 4 teams (8 each)}`

`text{16 boxes → (16 × 4) = 64 teams}`
 

`text{Strategy 2 (algebra):}`

`text(Let)\ n =\ text(number of teams)`

`8 xx n` `= 16 xx 32`
`:. n` `= (16 xx 32)/8`
`n` `= 2 xx 32`
  `= 64`

Number and Algebra, NAP-C2-38 SA

In an orchard there are 4 lemon trees for every 9 orange trees.

There are 81 orange trees.

How many lemon trees are in the orchard?
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`text(36 lemon trees)`

Show Worked Solution

`text(Check some numbers of orange trees:)`

`text(9 orange trees)\ ->\ text(4 lemon)`

`text(18 orange trees) -> 2 xx 4 = 8\ text(lemon)`

`text(27 orange trees) -> 3 xx 4 = 12\ text(lemon)`

`vdots`

`text(81 orange trees) -> 9 xx 4 = 36\ text(lemon)`

`:.\ text(There are 36 lemon trees.)`

Number and Algebra, NAP-F2-32

A supermarket sells yoghurt in packs.

One pack of yoghurt has 8 tubs.
 

Each pack cost $6.

What is the highest number of tubs that can be bought for $40?

`42` `48` `52` `56` `64`
 
 
 
 
 
Show Answers Only

`48`

Show Worked Solution
`text(Number of packs)` `= 40 ÷ 6`
  `= 6\ \ text(remainder)\ 4`

 

`=> 6\ text(packs can be bought)`

`:.\ text(Total tubs of yoghurt)` `= 6 xx 8`
  `= 48`

Number and Algebra, NAP-F2-30

Ten people share in a lottery prize of $5650.

They keep $550 each and give the rest to charity.

How much money in total do they have to give to charity?

`$5100` `$510` `$150` `$15`
 
 
 
 
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`$150`

Show Worked Solution

`text(Lottery payout to each person)`

`=5650/10`

`=$565`
 

`:.\ text(Total amount they give to charity)`

`=(565-550) xx 10`

`=$150`

Number and Algebra, NAP-F2-26 SA

Ivan and Novik receive pocket money each week.

Ivan gets $3 and Novik gets $7.

After 12 weeks, how much more pocket money has Novik received than Ivan?

$  
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`$48`

Show Worked Solution

`text(Novik receives $4 more each week.)`

`:.\ text(Extra money after 12 weeks)`

`= 12 xx 4`

`= $48`

Number and Algebra, NAP-C2-11

Joel is running a cooking class.

He has 26 students in the class and needs to give them 2 eggs each for a recipe.

Eggs are sold in cartons of 12.
 

 
What is the least number of egg cartons that Joel needs to buy?

`3` `4` `5` `6`
 
 
 
 
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`5\ text(cartons)`

Show Worked Solution

`text(Cartons required)`

`=(26 xx 2) ÷ 12`

`=52 -: 12`

`= 4\ 4/12`

 

`:.\ text(Joel needs to buy 5 egg cartons.)`

Number and Algebra, NAP-E2-38 SA

Katrina puts some Rubik's cubes and identical bolts end to end.

3 Rubik's cubes are the same length as 4 bolts.

Each Rubik's cube is 8 cm long.
 

 
How many centimetres long is each bolt?

   centimetres
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`6\ text(cm)`

Show Worked Solution

`text(Total length of 3 Rubik’s cubes)`

`= 3 xx 8`

`= 24\ text(cm)`
 

`:.\ text(Length of one bolt)`

`= 24 ÷ 4`

`= 6\ text(cm)`

Number and Algebra, NAP-E2-35 SA

Kurt, Shane and Harry collect guitars and own 70 guitars between them.

Kurt owns half as many as Shane.

Harry owns four times as many as Kurt.

How many guitars does Kurt own?
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`10`

Show Worked Solution

`text(Strategy one)`

`text(Try some values for Kurt:)`

`text(If Kurt has 5, Harry has 20, Shane has 10.)`

`=>\ text(i.e. a total of 35 guitars)`

`:.\ text(When Kurt has 10 guitars, there are 70 in total.)`

 

`text{Strategy two (using algebra)}`

`text(Expressing the information as equations:)`

`K + S + H = 70\ …\ (1)`

`K` `= 1/2 S`
`=> S` `= 2K\ …\ (2)`
`H` `= 4K\ …\ (3)`

 

`text{Substitute (2) and (3) into (1)}`

`K + 2K + 4K` `= 70`
`7K` `= 70`
`K` `= 10`

`:.\ text(Kurt owns 10 guitars.)`

Number and Algebra, NAP-E2-34 SA

Willy has 8 packets of lollipops.

There are 5 lollipops in each small packet.

There are 12 lollipops in each large packet.

Willy has 6 small packets.

How many lollipops does he have altogether?
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`54\ text(lollipops)`

Show Worked Solution

`text(S) text(ince Willy has 6 small packets`

`=>\ text(Willy has 2 large packets)`
 

`:.\ text(Total number of lollipops)`

`= (6 xx 5) + (2 xx 12)`

`=30+24`

`= 54`

Number and Algebra, NAP-F2-04

Five surfers owned a total of 58 surfboards between them.

Two of the surfers owned 20 surfboards each.

The other three, Lane, Gordon and Shelly, owned the same number of surfboards.

How many surfboards does Gordon own?

`6` `8` `12` `38`
 
 
 
 
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`6`

Show Worked Solution

`text(2 surfers own 20 boards each)\ = 40\ text(boards)`

`:.\ text(Surfboards owned by Gordon)`

`= (58-40) ÷ 3`

`=18 -: 3`

`= 6`

Number and Algebra, NAP-G2-35 SA

Archer has blocks with two square faces.

He builds the model below.
 

 
What is the height of the model in centimetres?

  centimetres
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`12\ text(cm)`

Show Worked Solution

`text(2 × length of block = 18 cm)`

`=>\ text(Length of 1 block = 9 cm)`

`=>\ text(Side length of the square face)`

`= 9 ÷ 3`

`= 3\ text(cm)`
 

`:.\ text(Height)` `= 3 xx 4`
  `= 12\ text(cm)`

Number and Algebra, NAP-G2-34 SA

In a card game, Shane gets 4 cards and earn points.
 

 
Each black triangle is worth double the points of each white triangle.

How many points is a white triangle worth?
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`5\ text(points)`

Show Worked Solution

`text(Shane’s hand is worth the same as having)`

`text(6 white triangles.)`

`6 xx`   `= 30`
`:.`     `= 30 ÷ 6`
     `= 5\ text(points)`

Number and Algebra, NAP-H2-40 SA

Grant was making a scale drawing of a pipeline on grid paper.

The full length of the pipeline is drawn below. Its construction requires 8 identical sections to be made and joined together (not shown on the diagram).
  

 
What is the length of each section of pipeline?

   metres
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`25`

Show Worked Solution
`text(S)text(ection length)` `= text(total length)/text(number of sections)`
  `= (5 xx 40)/8`
  `=200/8`
  `= 25\ text(metres)`

Number and Algebra, NAP-H2-23

Riley had 3 bird cages that each contained 12 birds.

He then bought one more bird cage and spread the birds out evenly between the 4 cages.

How many birds were then in each cage?

`6` `9` `10` `12`
 
 
 
 
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`9`

Show Worked Solution
`text(Total birds)` `= 3 xx 12`
  `= 36`

 

`:.\ text(Birds in each of 4 cages)`

`= 36 ÷ 4`

`= 9`

Number and Algebra, NAP-I2-36 SA

A group of 8 friends are planning a trip to Reptile World.

Lunch will cost $9 per person.

Entry will cost $16 per person.

Hiring a bus for transport will cost $250 for the whole group.

What is the expected total cost of the trip for the whole group?

$   
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`$450` 

Show Worked Solution
`text(Lunch cost)` `= 8 xx 9`
  `= $72`
`text(Entry cost)` `= 8 xx 16`
  `= $128`
`text(Bus hire)` ` = $250`

 

`:.\ text(Total cost)` `= 72 +128 + 250`
  `= $450`

Number and Algebra, NAP-D2-34

The Big Merino in Goulburn is 15 m tall.

Justin owns a real merino sheep that is 75 cm tall.
 

 
How many times taller is the Big Merino than Justin's merino?

 
 `15`
 
 `20`
 
 `30`
 
 `60`
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`20`

Show Worked Solution

`text(Converting the height of the big merino to cm)`

`=15 xx 100`

`=1500\ text(cm)`

 

`:.\ text(Times taller)` `=1500/75`
  `=(150 xx 10)/75`
  `=20`

Number and Algebra, NAP-D2-25

A tadpole is measured to be 9 mm long.

A few weeks later, the tadpole turns into a frog that is about 8 times longer than its tadpole length.

The difference between the length of the frog and its length as a tadpole is about

`text(1 mm)` `text(17 mm)` `text(63 mm)` `text(72 mm)`
 
 
 
 
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`text(63 mm)`

Show Worked Solution
`text(Length of frog)` `=8 xx 9`
  `=72\ text(mm)`
   
`:.\ text(Difference)` `= 72 – 9`
  `=63\ text(mm)`