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Number, NAP-L4-CA27 SA v1

Gary is painting his house over 3 days.

  • He paints `1/3` of the house on the first day.
  • He paints `5/12` of the house on the second day.

In order to finish, what percentage of the house does Gary need to paint on the third day?

     %
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`25 text(%)`

Show Worked Solution
`text(Fraction painted)` `= 1/3 + 5/12`
  `= (4 + 5)/12`
  `= 9/12`
  `=3/4`
  `=75 text(%)`

 
`:. 25 text(% needs to be painted on the third day.)`

Number, NAP-L3-NC03

Santana is buying a guitar string.

Some of the strings are on sale.

Select the string that will be cheapest.
 

 
 
 
 
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`text(Sale: take 20% off)`

Show Worked Solution

`text(C)text(ost of each option:)`

`$17`

`$35\ text(less 50%) = $17.50`

`text($20 less 20%) = 20 – 4 = $16`

`text($24 less 25%) = 24 – 6 = $18`

`:.\ text(Sale: take 20% off is the cheapest string.)`

Number, NAP-A4-CA14

The population of Australian states in 2015 and 2016 is recorded in the table below.

Some data for Western Australia is not shown.
 

 
What was the population of Western Australia (WA) close to in 2016?

`2\ 773\ 100` `2\ 710\ 500` `2\ 147\ 600` `2\ 091\ 300`
 
 
 
 
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`2\ 091\ 300`

Show Worked Solution

`text(WA Population in 2016)`

`= 2\ 085\ 021 xx 1.003`

`~~ 2\ 091\ 300`

Number, NAP-A4-CA09

There were only 17 students in Grace's class on Wednesday. The other 8 were absent.

What percentage of Grace's class was absent?

`text(8%)` `text(25%)` `text(32%)` `text(33%)`
 
 
 
 
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`32text(%)`

Show Worked Solution
`text(Total in class)` `= 17 + 8`
  `= 25`

 

`:.\ text(Percentage absent)`

`= 8/25 xx 100`

`= 32text(%)`

Number, NAP-J3-CA30 SA

Don buys a cricket ball, originally marked $30, that is discounted by 25%.

He also has a loyalty card that gives him another 20% off the sale price.

What is the final cost of the ball?

$  
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`$18`

Show Worked Solution

`text(Solution 1)`

`text(Sale price)` `= 30 – (25text(%) xx 30)`
  `=30 – 7.50`
  `= $22.50`

 

`:.\ text(Final cost)` `= 22.50 – (20text(%) xx 22.50)`
  `= $18`

 

`text{Solution 2 (advanced)}`

`text(Final cost)` `= 30 xx 0.75 xx 0.8 `
  `= $18`

Number, NAP-D3-CA23 SA

A scholarship fund of $1 000 000 is allocated between three scholarships as shown in the table below.
 

 
150 students were given a Hardship Scholarship.

How much did each Hardship Scholarship winner get?

$   
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`$2000`

Show Worked Solution

`text(Hardship Scholarship Funds)`

`= 30text(%) xx 1\ 000\ 000`

`= $300\ 000`
 

`:.\ text(Amount each winner received)`

`= (300\ 000)/150`

`= $2000`

Number, NAP-F3-CA28 SA

Richard bought a second hand snowboard at a cost of $390.

Richard had to spend 65% of his savings to buy the snowboard.

How much did Richard have in his savings after buying the snowboard?

$ 
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`$210`

Show Worked Solution
`65text(%) xx text(Savings)` `= $390`
 `:.\ text(Savings)` `= 390/0.65`
  `= $600`

 

`:.\ text(Savings left)` `= 600 – 390`
  `= $210`

Number, NAP-B3-NC18

A local soccer club has 1600 fans.

At a game, one-quarter of the fans wear a yellow jersey and the rest wear red.

25% of the red jerseys have a black stripe down the back.

How many red jerseys have a black stripe?

`250` `300` `400` `1200`
 
 
 
 
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`300`

Show Worked Solution
`text(Total red jerseys)` `=3/4 xx 1600`
  `=1200`

 

`:.\ text(Red jerseys with black stripe)`
`=0.25 xx 1200`
`=300`

Number, NAP-E3-NC15

Hoon's camera has a memory card that holds 20 gigabytes.

He has used exactly 16 gigabytes of memory.

What percentage of the memory has not been used?

`text(4%)` `text(20%)` `text(25%)` `text(40%)` `text(75%)`
 
 
 
 
 
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`text(20%)`

Show Worked Solution
`text(Memory left)` `= 20 – 16`
  `= 4\ text(GB)`

 

`:.\ text(Percentage not used)`

`= 4/20`

`= 20text(%)`

Number, NAP-C3-CA11

In a water polo season, Vladimir had 330 shots at goal.

He scored 170 goals but missed the rest.

Vladimir's success rate of scoring goals was?

 
 less than 25%
 
 more than 25% but less than 50%
 
 more than 50% but less than 75%
 
 more than 75%
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`text(more than 50% but less than 75%)`

Show Worked Solution
`text(Success rate)` `=170/330`
  `=0.515…`
  `=52text(%)`

 

`:.\ text(His succes rate is more than 50% but less than 75%.)`

Number, NAP-H3-CA28 SA

Harrison was saving his money to buy a cricket bat.

After 1 month, he had saved 45% of the bat's cost.

After 2 months, he had saved another $90 and now had 75% of the bat's cost.

How much does the bat cost?

$  
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`$300`

Show Worked Solution
`text(75%)\ -\ text(45%)` `= $90`
`text(30%)` `= $90`
`:. 1text(%)` `= $3`

 

`:.\ text(The bat cost)` `= 100 xx 3`
  `= $300`