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Number, NAP-L4-NC05 SA

A menu requires 600 grams of curry paste.

Three satchels are emptied that provide 120 grams of curry paste.

How many more satchels are required?

 
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`12`

Show Worked Solution
`text(Paste per satchel)` `= 120/3 = 40\ text(grams)`
`text(Total satchels required)` `= 600/40`
  `= 15 `

 
`:.\ text(An extra 12 satchels are required.)`

Number, NAP-L4-CA31

Earthquakes are measured using the Richter scale which calculates the amount of energy (in ergs) the earthquake releases.

An earthquake measuring 4 on the Richter scale releases `32^4` ergs of energy.

An earthquake measuring 8 on the Richter scale releases `32^8` ergs of energy.

An earthquake measuring 8 on the Richter scale releases how many times as much energy as an earthquake measuring 4?

`10^2` `10^4` `32^2` `32^4`
 
 
 
 
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`32^4`

Show Worked Solution

`text(Energy)\ (4) = 32 xx 32 xx 32 xx 32\ text(ergs)`

`text(Energy)\ (8) = 32 xx 32 xx 32 xx 32 xx 32 xx 32 xx 32 xx 32\ text(ergs)`

 
`:.\ text{Times of energy (8 ÷ 4)}`

`= 32^8/32^4`

`= 32^4`

Number, NAP-L4-CA34 SA

A laundromat can wash 12 loads of laundry in one hour at full capacity.

A standard load of laundry weighs 7 kilograms.

Here is some information about two different washing machines.
 


 

Working at full capacity, how many litres of water would the laundromat expect to save in one hour by using the front loader instead of the top loader?

    litres
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`text(315 L)`

Show Worked Solution

`text(Top loader water used (1 load))`

`= 7 xx 10.25`

`= 71.75\ text(L)`
 

`text(Front loader water used (1 load))`

`= 7 xx 6.5`

`= 45.5\ text(L)`
 

`:.\ text(Expected water saved)`

`= 12 xx (71.75 – 45.5)`

`= 315\ text(L)`

Number, NAP-L4-CA33 SA

Genghis and Kublai are shooting arrows at a target.

Genghis shoots an arrow every 3 seconds.

Kublai shoots an arrow every 8 seconds.

They shoot their first arrow together at 10:00 am.

How many more times will they shoot arrows at exactly the same time in the next 3 minutes?

 
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`7`

Show Worked Solution

`text(Every 24 seconds, arrows shot at the same time.)`

`=>\ text(Arrows are shot at the same time:)`

`24, 48, 72, 96, 120, 144, 168\ text(seconds)`

`:. 7\ text{more times  (time ≤ 180 seconds)}`

Number, NAP-K4-CA11

Brendan lives in New York and returns to visit his hometown, Perth, every three years.

His next visit in 2020 will also let him attend the Mining Expo that is held once every two years.

When was the last year that Brendan visited Perth at the same time as the Mining Expo was held?

2014 2015 2016 2017
 
 
 
 
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`2014`

Show Worked Solution

`text(Brendan visits to Perth:)`

`2020, 2017, 2014, 2011`

`text(Mining Expo held in years:)`

`2020, 2018, 2016, 2014`
 

`:. 2014\ text(was the most recent year.)`

Number, NAP-A3-CA27 SA

Patrick uses 25 litres of water every minute when he has a shower.

Kate uses 150 litres of water when she has a bath.

How many less litres of water does Patrick use in a  `5 1/2`  minute shower than Kate's bath?

    litres
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`12.5\ text(litres)`

Show Worked Solution

`text(Patrick water usage)`

`= 5.5 xx 25`

`= 137.5\ text(litres)`
 

`:.\ text(Less usage)` `= 150 – 137.5`
  `= 12.5\ text(litres)`

Number, NAP-C4-CA25

Harry sold one schnitzel wrap every 4 minutes at a surfing competition.
 

 
At this rate, how many minutes would it take to sell $320 worth of schnitzel wraps?

 
 `text(25 minutes)`
 
 `text(50 minutes)`
 
 `text(80 minutes)`
 
 `text(200 minutes)`
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`text(200 minutes)`

Show Worked Solution
`text(Total wraps sold)` `= 320 ÷ 6.40`
  `= 50`

 

`:.\ text(Minutes to sell $320 worth)`

`= 50 xx 4`

`= 200\ text(minutes)`

Number, NAP-D4-CA17

A health food packet had the following information on its label.
 

 
What was the mass of the health food packet to the nearest gram?

`1328\ text(grams)` `990\ text(grams)` `698\ text(grams)` `578\ text(grams)`
 
 
 
 
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`578\ text(grams)`

Show Worked Solution

`text(Multiple of 100 grams in one packet:)`

`844 ÷ 146 = 5.78…`

`5.78 xx 100 = 578.08…`

`:.\ text(The mass of the packet is about 578 grams.)`

Number, NAP-D3-CA31 SA

Saul's workshop requires lighting for 30 hours per week, every week of the year.

He uses globes that need replacing after 10 000 hours of use.

After how long, to the nearest year, would Saul need to replace any individual globe?

   years
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`text{6 years (nearest year)}`

Show Worked Solution

`text(Usage per year of one globe)`

`= 30 xx 52`

`= 1560`
 

`:.\ text(Time until replacement of globe)`

`= (10\ 000)/1560`

`= 6.41…`

`= 6\ text{years (nearest year)}`

Number, NAP-F4-NC30 SA

Marshall keeps a tin of lollipops on his desk at home.

His son Dallas takes 1 lollipop out every 3 days.

Marshall adds a new lollipop to the tin every 4 days.

The lollipops in Marshall's tin are decreasing by 1 lollipop every `x` days.

What is the value of  `x`?
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`12`

Show Worked Solution

`text(Every 12 days, Dallas takes 4 lollipops)`

`text(and Marshall adds 3.)`

`:. x = 12`

Number, NAP-F4-NC20 SA

It takes Kate 15 seconds to place a brochure in an envelope and seal it.

How many minutes will it take her to pack and seal 10 envelopes?

   minutes
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`2.5`

Show Worked Solution
`text(Time)` `=10 xx 15`
  `=150\ text(seconds)`
  `=2.5\ text(minutes)`

Number, NAP-G4-NC22

Alice has 5 guinea pigs.

They eat 200 grams of cabbage per day, in total.

How many grams of cabbage would 1 guinea pig eat in one week?

`40\ text(grams)` `280\ text(grams)` `1400\ text(grams)` `2800\ text(grams)`
 
 
 
 
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`text(280 grams)`

Show Worked Solution

`text(Cabbage eaten by 1 guinea pig in 1 day)`

`=200/5`

`=40\ text(grams)`

`:.\ text(Cabbage eaten by 1 guniea pig in 1 week)`

`=7 xx 40`

`= 280\ text(grams)`

Number, NAP-G4-CA24

Scientists estimate that in 1 km² of swamp, 30 000 mosquito eggs are laid every minute.

Which value is the closest to the number of mosquito eggs that would be laid in one day?

`7.2 xx 10^4` `7.2 xx 10^5` `4.32 xx 10^5` `4.32 xx 10^7`
 
 
 
 
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`4.32 xx 10^7`

Show Worked Solution

`text(Total eggs laid in one day)`

`= 30\ 000 xx 60 xx 24`

`=4.32 xx 10^7`

Numbers, NAP-H4-NC23 SA

It takes 2 people 10 hours to pick 800 lettuces during harvesting.

At the same rate, how many hours should it take for 5 people to pick 1200 lettuces?

   hours
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`6\ text(hours)`

Show Worked Solution

`text(It takes 20 hours to pick 800 lettuces.)`

`:.\ text(1 person can pick)\ \ 800/20 = 40\ text(lettuces per hour)`

`:. 5\ text(people pick 200 lettuces per hour)`

`:.\ text{Time to pick 1200 lettuces (5 people)}` 

`= 1200/200`

`= 6\ text(hours)`

Number, NAP-H4-NC19 SA

Paul stacks milk cartons into supermarket refrigerator shelves.

Each shelf is stacked with 6 full cream milk cartons, 4 lite milk cartons and 2 skim milk cartons.

Every hour Paul stacks 240 milk cartons in total.

How many lite milk cartons does he stack every hour?
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`80`

Show Worked Solution

`text(Shelves stacked each hour)`

`= 240/12`

`= 20`

 

`:.\ text(Lite milk cartons stacked)`

`= 20 xx 4`

`= 80\ text(per hour.)`

Number, NAP-H4-CA22

It takes 15 minutes for all of the sand to flow through a sand timer.

The sand timer contains 475 grams of sand.

Each millilitre of sand weighs 1.5 grams.
 

 naplan-2015-22

 
How many millilitres of sand flow through the timer per minute?

`10.3` `21.1` `31.7` `47.5`
 
 
 
 
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`21.1`

Show Worked Solution

`text(Total millilitres) = 475/1.5 = 316.67…`

 

`text(Sand flow)` `= (316.67…)/15`
  `= 21.1\ text(ml per minute)`