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Algebra, NAP-L4-CA12

A kayak can be hired for different numbers of hours, as shown in the table below.

Select the answer that shows how to calculate the cost of hiring a kayak.

 
number of hours multiplied by $30
 
$10 for every hour plus an extra $30
 
number of hours multiplied by $10
 
$10 for every hour plus an extra $20
Show Answers Only

`text($10 for every hour plus an extra $20)`

Show Worked Solution

`text($10 for every hour plus $20)`

`text(Test):`

`2\ text(hours) = 2 xx 10 + 20 = $40`  ✔

`5\ text(hours) = 5 xx 10 + 20 = $70`  ✔

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 7, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-K4-CA23

A biscuit factory produces 72 000 packets of biscuits in a year.

Production is expected to increase by 1500 packets each year.

Which of these will give the best estimate of the production of the biscuit factory in 3 years' time?

 
`72\ 000 + 1500 xx 3`
 
`(72\ 000 + 1500) xx 3`
 
`72\ 000 + 1500 + 3`
 
`(72\ 000 + 3) xx 1500`
Show Answers Only

`72\ 000 + 1500 xx 3`

Show Worked Solution
`text(Estimate)`  `= 72\ 000+ 1500 + 1500 + 1500` 
  `= 72\ 000 + 1500 xx 3`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 9, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-A4-NC25

In a set of five consecutive whole numbers, the largest number is given the value `h`.

The smallest number in the set has a value of

`h + 4` `5 - h` `h - 5` `h - 4`
 
 
 
 
Show Answers Only

`h – 4`

Show Worked Solution

`text(Numbers in descending order are:)`

`h , h – 1, h – 2, h – 3, h – 4`

`:.\ text(Smallest number is)\ \ h – 4`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 9, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-C4-CA22

Richard is ascending in a hot air balloon.

The temperature drops by the same amount every 50 metres that Richard ascends.
 

 
At ground level the temperature is 31°C.

At a height of 600 metres, the temperature is –5°C.

What is the air temperature at a height of 200 metres?

`text(16°C)` `text(18°C)` `text(19°C)` `text(22°C)`
 
 
 
 
Show Answers Only

`text(19°C)`

Show Worked Solution

`text(There are)\ 12 xx 50\ text(m distances in 600 m.)`

`text(Temperature drop each 50 m)`

`= {31 – (-5)}/12`

`= 36/12`

`= 3°`
 

`:.\ text(Temperature at 200 m)`

`= 31 – (4 xx 3)`

`= 19\ text(°C)`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 9, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-C4-NC05

Australia Post use formulas to calculate the cost of boxes sent in the post to local destinations.

They calculate the size of the box by the formula:
 

size = width + height + length

 
The minimum postage applies to boxes with a size of 110 cm or less.

Which box below is oversized?

  Length (cm) Height (cm) Width (cm)
 
40 40 20
 
60 10 45
 
50 20 40
 
40 40 30
Show Answers Only

`60 + 10 + 45 = 115`

Show Worked Solution

`text(Consider the calculation for each option:)`

`text(Option 1:  40 + 40 + 20 = 100 cm)`

`text(Option 2:  60 + 10 + 45 = 115 cm)`

`text(Option 1:  50 + 20 + 40 = 110 cm)`

`text(Option 1:  40 + 40 + 30 = 110 cm)`

 

`:.\ text(The  60 + 10 + 45  box is oversized.)`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 6, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-E4-NC11

Zoe collected 8 baskets of eggs from her chicken coup.

Each basket had the same number of eggs and a total of 96 eggs were collected.

Which equation shows the average number of eggs,  `x`,  in each basket?

 
`x = 96 xx 8`
 
`x = 96 - 8`
 
`x ÷ 8 = 96`
 
`x xx 8 = 96`
Show Answers Only

`x xx 8 = 96`

Show Worked Solution
`text(Eggs per basket) ` `= text(total eggs)/text(number of baskets)`
`x` `= 96/8`
`:. x xx 8` `= 96`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 7, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-G4-NC14

Aaron has $3 less than Brendon. 

Using  `a`  for Aaron's money and  `b`  for Brendon's money, which equation correctly describes this fact?

`a = b + 3` `a = 3 - b` `a = b - 3` `a = b ÷ 3`
 
 
 
 
Show Answers Only

`a = b – 3`

Show Worked Solution

`a = b – 3`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 7, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-H4-CA20

Package Delivery Pty Ltd charges the following for delivering a package with mass  `x`  kg

`text(Price) = 9 + 4.5x`

What is the mass, in kg, of a package that costs $90 to deliver?

`10` `18` `20` `22`
 
 
 
 
Show Answers Only

`20`

Show Worked Solution
`9+4.5x` `=90`
`4.5x` `=81`
`x` `=81/4.5`
  `=20`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 9, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-I4-NC13

Ryan and Oliver are buying goldfish for their fish tank.

Oliver buys 3 times the number of goldfish as Ryan does, plus another 5.

Let `m` be the number of goldfish that Ryan buys.

Which expression represents the number of goldfish Oliver buys?

`(3 xx m) + 5` `3 + (5 xx m)` `(m ÷ 3) - 5` `3 - (m ÷ 5)`
 
 
 
 
Show Answers Only

`(3 xx m) + 5`

Show Worked Solution

`text(Goldfish bought by Oliver)`

`= (3 xx m) + 5`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 7, smc-3179-50-Word problems, smc-683-50-Word problems

Algebra, NAP-I4-NC08

Ali joins a gym that has a fortnightly fee of $33.

Members pay an extra $12 per session if they want to do a special yoga class.

Which expression represents Ali's fortnightly gym bill if she does  `x`  yoga classes during the fortnight?

`12x` `33x` `33x + 12` `33 + 12x`
 
 
 
 
Show Answers Only

`33 + 12x`

Show Worked Solution
`text(Fortnightly cost)` `=\ text(fee + yoga classes)`
  `=\ 33 + 12x`

Filed Under: Basic Algebra, Basic Algebra, Financial Maths, Financial Maths Tagged With: Band 7, smc-3174-30-Profit/Cost/Revenue, smc-3179-50-Word problems, smc-683-50-Word problems, smc-892-30-Profit/Cost/Revenue

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