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Number, NAPX-I4-CA22 SA

There are 32 people in a meeting room.

The ratio of females to males in the room is 9 to 7.

How many females need to leave the room so that the ratio of females to males in the room is 1 to 1?
Show Answers Only

`4\ text(females)`

Show Worked Solution

`text(Females : Males) = 9 : 7`

`=> 18\ text(females and 14 males are in the room.)`

 

`:.\ text(If 4 females leave, the ratio)`

`text(becomes 1 : 1)`

Number, NAPX-I4-CA05 SA

Chakra earns $23.88 per hour at a homewares shop.

In one week, she worked `15 1/4` hours.

She used the money to buy incense scented candles for her friends.

Each candle costs $31.25.

What is the maximum number of candles Chakra can buy?

   candles
Show Answers Only

`11`

Show Worked Solution
`text(Money earned)` `= 15 1/4 xx 23.88`
  `= $364.17`

 

`:.\ text(Maximum candles)` `= 364.17/31.25`
  `= 11.65…`
  `= 11\ text{candles (must round down)}`

Number, NAPX-J4-NC07 SA

An African wildlife reserve has 480 elephants.

Of the 480 elephants, `5/8` of them weigh more than 4000 kilograms.

Of the elephants that weigh more than 4000 kilograms, `1/4` weigh more than 6000 kilograms.

How many elephants in the reserve weigh more than 6000 kilograms?
Show Answers Only

`75`

Show Worked Solution

`text(Number of elephants > 4000 kg)`

`= 5/8 xx 480`

`= 300`

 

`text(Number of elephants > 6000 kg)`

`= 1/4 xx 300`

`= 75`

Number, NAPX-J4-NC05 SA

Manou's French restaurant took in $8321.70 on Valentine's Day.

Pete's Paleo restaurant took in $3190.85 on the same night.

How much more money did Manou's restaurant take in than Pete's on Valentine's Day?

$   
Show Answers Only

`$5130.85`

Show Worked Solution

`$8321.70 – $3190.85`

`= $5130.85`

Number, NAPX-J4-NC03 SA

Harmony is buying eggs for her vegetarian restaurant.

Each carton contains 12 eggs.

If she needs 86 eggs, how many cartons will she need to buy?
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`text(8 cartons)`

Show Worked Solution

`86 ÷ 12 = 7\ text(remainder 2)`

`:.\ text(Harmony need 8 cartons.)`

Algebra, NAPX-J4-CA40 SA

Sierra creates a muesli which is a mixture of 4 different types of fruit and nuts.

She makes 400 grams of the mixture and weighs each ingredient as follows:

  • 40% of the mixture is macadamias.
  • The rest of the mixture is made up of walnuts, apricots and raisins.
  • The mass of walnuts is the same as the mass of apricots.
  • The mass of walnuts is twice the mass of raisins.

How many grams of apricots are in the 400 grams of muesli?

 

Show Answers Only

`96\ text(grams)`

Show Worked Solution
`text(Mass of macadamias)` `= 40 text(%) xx 400`
  `= 160\ text(grams)`

 

`text(Weight of remaining ingredients)`

`= 400-160`

`= 240\ text(grams)`

 

`text(Let)\ \ x = text(weight of apricots)`

`x + x + 1/2x` `= 240`
`:. x` `= 240/2.5`
  `= 96\ text(grams)`

Measurement, NAPX-J4-CA39 SA

A rectangular prism is made by stacking 6 identical triangular prisms, as pictured below.
 

 
What is the volume of one triangular prism, in cubic centimetres?

 cubic centimetres
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`27\ 552 text(cm³)`

Show Worked Solution

`text(Volume of rectangular prism)`

`= 42 xx 48 xx 82`

`= 165\ 312\ text(cm³)`

 

`:.\ text(Volume of 1 triangular prism)`

`= 165\ 312 ÷ 6`

`= 27\ 552\ text(cm³)`

Measurement, NAPX-J4-CA37 SA

Sequoia owns a farm with a rectangular paddock.

She increases the area of the paddock by adding land that changes it into the shape of a trapezium.
 

 
What is the area of Sequoia's new paddock, in square metres?

  square metres
Show Answers Only

`2599\ text(m²)`

Show Worked Solution
`A` `= 1/2h(a + b)`
  `= 1/2 xx 46 xx (42 + 71)`
  `= 2599\ text(m²)`

Algebra, NAPX-J4-CA36 SA

In this inequality `n` is a whole number.

`5/n < 3/5`

What is the smallest possible value for `n` to make this inequality true?
Show Answers Only

`9`

Show Worked Solution
`5/n` `< 3/5`
`3n` `> 25`
`n` `> 25/3`
`n` `> 8.33…`

 

`:.\ text(Smallest)\ n = 9`

Number, NAPX-J4-CA35 SA

The sale price of a second hand car is $4800.

Zilda buys the car for 25% off the sale price.

Zilda has a discount voucher that gives her a further $240 off the sale price.

What percentage of the original price does Zilda pay for the car?

 %
Show Answers Only

`text(70%)`

Show Worked Solution
`text(Sale price)` `= $4800-(25% xx 4800)`
  `= 75% xx 4800`
  `= $3600`

 

`text(Purchase price)` `= 3600-240`
  `= $3360`

 

`:.\ text(Percentage of original price)`

`= 3360/4800 xx 100`

`= 70 text(%)`

Number, NAPX-J4-CA33 SA

Huckleberry opens a savings account and deposits $1200 into it.

He makes no more deposits and earns simple interest on his original deposit at 2.5% each year.

How much interest will Huckleberry earn after 3 years?

$ 
Show Answers Only

`$90`

Show Worked Solution
`text(Interest earned)` `= Prn`
  `= 1200 xx 2.5/100 xx 3`
  `= $90`

Number, NAPX-J4-CA30 SA

Skye sells 18 mini-cakes of soap at the farmers market for a total of $9.90.

Dharma sells 30 cakes of soap at the same price per cake of soap as Skye.

In total, how much more does Dharma make than Skye?

$ 
Show Answers Only

`$6.60`

Show Worked Solution
`text(C)text(ost of 1 soap)` `= 9.90 ÷ 18`
  `= $0.55`
`text(C)text(ost of 30 soaps)` `= 30 xx 0.55`
  `= $16.50`

 

`:.\ text(Extra sales)` `= 16.50-9.90`
  `= $6.60`

Algebra, NAPX-J4-CA29 SA

Indigo is a lawyer.

She charges $250 to look at a case and then a fixed price for each minute she spends on the case.

The graph below shows Indigo's charge based on the number of minutes she spends on the case.
 

 
How much will Indigo charge for a case that takes 60 minutes of her time?

$ 
Show Answers Only

`$430`

Show Worked Solution

`text(Initial charge = $250)`

`text(From the graph,)`

`=>\ text(50 minute matter costs $400)`

`:.\ text(C)text(ost per minute)` `= (400-250)/50 = $3`

 

`:.\ text(C)text(ost of 60 minute matter)`

`= 250 + 60 xx 3`

`= $430`

Number, NAPX-J4-CA26 SA

A candle maker increases the price of a candle from $20 to $25.

What is the percentage increase in his price?

 %
Show Answers Only

`text(25%)`

Show Worked Solution

`text(Price increase) = 25 – 20 = $5`

`text(Percentage increase)` `= 5/20 xx 100`
  `= 0.25 xx 100`
  `= 25text(%)`

Statistics and Probability, NAPX-J4-CA24 SA

Fifty football fans were surveyed about modes of transport they took to get to the game.

  • 22 caught a train
  • 21 caught a bus
  • 20 didn't take a train or a bus.

The diagram is missing some information.
 

 
How many caught both a train and a bus to get to the game?
Show Answers Only

`13`

Show Worked Solution

`text(Interpreting the Venn diagram:)`

`text(S)text(ince fifty fans surveyed,)`

  • `text(20 didn’t take either train or bus)`
  • `text(9 caught train only)`
  • `text(8 caught bus only)`

`:.\ text(Number that took both train and bus)`

`= 50 – (20 + 9 + 8)`

`= 13`

Measurement, NAPX-H4-CA32 SA

Mickey cuts a quarter circle out of a full circle, as shown below.
 

 
If the circle's radius is 7 cm, what is the perimeter of the shape, to the nearest centimetre?

   cm
Show Answers Only

`47\ text{(nearest cm)}`

Show Worked Solution
`text(Perimeter)` `=\ text(arc + 2 × radii)`
  `= (3/4 xx 2 xx pi xx r) + 2 r`
  `= 3/4 xx 2 xx pi xx 7 + 2 xx 7`
  `= 46.986…`
  `= 47\ text{cm  (nearest cm)}`

Statistics and Probability, NAPX-J4-CA34 SA

Ziggy throws darts at a board split into 4 sections and records which section they hit.
 

 
Based on Ziggy's data, what is the probability that a dart he throws will land in section 1 or 2?

Express your answer as a percentage rounded to the nearest tenth.

 %
Show Answers Only

`text{75.3% (nearest tenth)}`

Show Worked Solution
`text(Number of throws)` `= 45 + 22 + 13 + 9`
  `= 89`

 

`:.\ text{Probability (1 or 4)}` `= {(45 + 22)}/89`
  `= 67/89`
  `= 0.7528…`
  `= 75.3 text{% (nearest tenth)}`