smc-3148-70-Rates

Number, NAP-I3-CA17v1

A brewery can make 1250 cans of ale and 900 cans of lager per hour.

The brewery runs non-stop and each can weighs 350 grams.

How many kilograms of ale and lager, altogether, does the brewery make in 1 full day?

	`226\ text(kilograms)`
	`753\ text(kilograms)`
	`18\060\ text(kilograms)`
	`21\ 240\ text(kilograms)`

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`18\060\ text(kilograms per day)`

Show Worked Solution

`text(Total cans made per hour)`

`=1250 + 900`

`= 2150`

`text(Kilograms made in 1 hour)`

`=2150 xx 350`

`= 752\ 500\ text(grams)`

`= 752.5\ text(kilograms)`

`:.\ text(Kilograms made in 1 day)`	`=752.5 xx 24`
	`=18\ 060`

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-L3-NC07 SA

A solar panel grid on a school roof produces an average of 8.6 kWh of energy per day.

How much energy will the grid produce for the school on average over 7 days?

kWh

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`60.2`

Show Worked Solution

`text(One multiplication strategy:)`

`7xx8=56`

`7 xx 0.6 = 4.2`

`7 xx 8.6 = 56+4.2=60.2`

`:.\ text(It produces 60.2 kWh over 7 days.)`

Number, NAP-L3-CA36 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-L3-CA34 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-A3-CA11 SA

A ute uses an average of 12 litres of diesel fuel for every 100 km travelled.

At this rate, how many litres would the ute use to travel 450 km?

litres

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`54\ text(litres)`

Show Worked Solution

`text(Litres used)`	`=\ text(litres per 100 km × multiples of 100 km)`
	`= 12 xx 4.5`
	`= 54\ text(litres)`

Number, NAP-F3-CA26 SA

Kate buys a new computer.

The disk in its hard drive makes 120 full turns every second.

How many minutes will it take for the disk to make 324 000 full turns?

minutes

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`45\ text(minutes)`

Show Worked Solution

`text(Turns in 1 minute)`

`= 120 xx 60`

`= 7200`

`:.\ text(Minutes needed)`

`= (324\ 000)/7200`

`= 45\ text(minutes)`

Number, NAP-E3-NC27 SA

Nona makes maple syrup on her farm.

The mass of 400 millilitres of her maple syrup is 600 grams.

How many litres is 2.4 kilogram of Nona's maple syrup?

litres

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`1.6\ text(litres)`

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`text(Multiples of 600 grams in 2.4 kilograms:)`

`=> 2400/600 = 4`

`:.\ text(Volume of maple syrup)`

`= 4 xx 400\ text(mL)`

`= 1600\ text(mL)`

`= 1.6\ text(litres)`

Number, NAP-G3-NC21 SA

Constance used 300 grams of sugar to make 12 brownies.

How many grams of sugar will she need to make 18 brownies?

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`text(450 grams)`

Show Worked Solution

`text(Sugar to make 18 brownies)`

`=18/12 xx 300`

`=1.5 xx 300`

`=450\ text(grams)`

Number, NAP-G3-CA31 SA

One litre of softdrink contains 90 grams of sugar.

How many millilitres of softdrink contain 4.5 grams of sugar?

millilitres

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`50`

Show Worked Solution

`text(Millilitres)`	`= 4.5/90 xx 1000\ text(mL)`
	`= 50\text(mL)`

Number, NAP-G3-CA26 SA

Ten nails have a mass of 22 grams.

How many nails would have a mass of 550 grams?

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`250\ text(nails)`

Show Worked Solution

`text(Mass of 1 nail)`	`=22/10`
	`= 2.2\ text(grams)`

`:.\ text(Nails in 550 grams)`	`= 550/2.2`
	`= 250\ text(nails)`

Number, NAP-I3-CA30 SA

Kurt is travelling from Newcastle to Sydney. The journey is 165 kilometres.

His car uses 8.35 litres of fuel per 100 kilometres.

How much fuel will Kurt need to make the journey?

Round your answer to the nearest litre.

litres

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`14\ text{litres (nearest whole)}`

Show Worked Solution

`text(Fuel needed)`	`= 165/100 xx 8.35`
	`= 13.77…`
	`= 14\ text{litres (nearest whole)}`

Number, NAP-I3-CA02

Scott owns a sheep station.

He keeps 4 sheep on every acre of the property.

How many acres would he need for 12 sheep?

`3`	`4`	`16`	`48`

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`3`

Show Worked Solution

`text(4 sheep per acre)`

`:.\ text(Acres needed for 12 sheep)`	`=12/4`
	`=3\ text(acres)`

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-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.)`